400 (number)


400 is the natural number following 399 and preceding [|401].

Mathematical properties

400 is the square of 20. 400 is the sum of the powers of 7 from 0 to 3, thus making it a repdigit in base 7.
A circle is divided into 400 grads, which is equal to 360 degrees and 2π radians..
400 is a self number in base 10, since there is no integer that added to the sum of its own digits results in 400. On the other hand, 400 is divisible by the sum of its own base 10 digits, making it a Harshad number.

Other fields

Four hundred is also

400s

401

A prime number, tetranacci number, sum of seven consecutive primes, sum of nine consecutive primes, Chen prime, Eisenstein prime with no imaginary part, Mertens function returns 0, member of the Mian–Chowla sequence.
402 = 2 × 3 × 67, sphenic number, nontotient, Harshad number,
403 = 13 × 31, Mertens function returns 0.
404 = 22 × 101, Mertens function returns 0, nontotient, noncototient.
405 = 34 × 5, Mertens function returns 0, Harshad number;
406 = 2 × 7 × 29, sphenic number, triangular number, centered nonagonal number, nontotient
407 = 11 × 37,
408 = 23 × 3 × 17
409 is a prime number, Chen prime, centered triangular number.

410

410 = 2 × 5 × 41, sphenic number, sum of six consecutive primes, nontotient, Harshad number
411 = 3 × 137, self number,
412 = 22 × 103, nontotient, noncototient, sum of twelve consecutive primes
413 = 7 × 59, Mertens function returns 0, self number
414 = 2 × 32 × 23, Mertens function returns 0, nontotient, Harshad number
415 = 5 × 83,
416 = 25 × 13
417 = 3 × 139
418 = 2 × 11 × 19, sphenic number,
A prime number, Sophie Germain prime, Chen prime, Eisenstein prime with no imaginary part, highly cototient number, Mertens function returns 0

420

421

422 = 2 × 211, Mertens function returns 0, nontotient

423

423 = 32 × 47, Mertens function returns 0, Harshad number
424 = 23 × 53, sum of ten consecutive primes, Mertens function returns 0, refactorable number, self number

425

425 = 52 × 17, pentagonal number, sum of three consecutive primes, Mertens function returns 0, the second number that can be expressed as the sum of two squares in three different ways.
426 = 2 × 3 × 71, sphenic number, nontotient,

427

427 = 7 × 61, Mertens function returns 0

428

428 = 22 × 107, Mertens function returns 0, nontotient
429 = 3 × 11 × 13, sphenic number, Catalan number

430s

430

430 = 2 × 5 × 43, sphenic number, untouchable number

431

A prime number, Sophie Germain prime, sum of seven consecutive primes, Chen prime, Eisenstein prime with no imaginary part
432 = 24 × 33 = 42 × 33, The sum of four consecutive primes, a highly totient number, sum of totient function for first 37 integers. 432! is the first factorial that is not a Harshad number in base 10. 432 is also three-dozen sets of a dozen, making it three gross. An equilateral triangle whose area and perimeter are equal, has an area equal to.

433

A prime number, Markov number, star number.
434 = 2 × 7 × 31, sphenic number, sum of six consecutive primes, nontotient

435

435 = 3 × 5 × 29, sphenic number, triangular number, hexagonal number, self number

436

436 = 22 × 109, nontotient, noncototient

437

437 = 19 × 23

438

438 = 2 × 3 × 73, sphenic number, Smith number.
A prime number, sum of three consecutive primes, sum of nine consecutive primes, strictly non-palindromic number

440s

440

440 = 23 × 5 × 11, the sum of the first seventeen prime numbers, Harshad number,
441 = 32 × 72 = 212
442 = 2 × 13 × 17, sphenic number, sum of eight consecutive primes

443

A prime number, Sophie Germain prime, Chen prime, Eisenstein prime with no imaginary part, Mertens function sets new low of -9, which stands until 659.
444 = 22 × 3 × 37, refactorable number, Harshad number.

445

445 = 5 × 89

446

446 = 2 × 223, nontotient, self number

447

447 = 3 × 149

448

448 = 26 × 7, untouchable number, refactorable number, Harshad number

449

A prime number, sum of five consecutive primes, Chen prime, Eisenstein prime with no imaginary part, Proth prime. Also the largest number whose factorial is less than 101000

450s

450

450 = 2 × 32 × 52, nontotient, sum of totient function for first 38 integers, refactorable number, Harshad number,
451 = 11 × 41; 451 is a Wedderburn–Etherington number and a centered decagonal number; its reciprocal has period 10; 451 is the smallest number with this period reciprocal length.
452 = 22 × 113
453 = 3 × 151

454

454 = 2 × 227, nontotient, a Smith number

455

455 = 5 × 7 × 13, sphenic number, tetrahedral number
456 = 23 × 3 × 19, sum of a twin prime, sum of four consecutive primes, centered pentagonal number

457

458 = 2 × 229, nontotient

459

459 = 33 × 17

460

460 = 22 × 5 × 23, centered triangular number, dodecagonal number, Harshad number, sum of twelve consecutive primes

461

A prime number, Chen prime, sexy prime with 467, Eisenstein prime with no imaginary part

462

462 = 2 × 3 × 7 × 11, binomial coefficient, sum of six consecutive primes, pronic number, sparsely totient number

463

A prime number, sum of seven consecutive primes, centered heptagonal number,
464 = 24 × 29, primitive abundant number
465 = 3 × 5 × 31, sphenic number, triangular number, member of the Padovan sequence, Harshad number

466

466 = 2 × 233, noncototient

467

A prime number, safe prime, sexy prime with 461, Chen prime, Eisenstein prime with no imaginary part

468

468 = 22 × 32 × 13, sum of ten consecutive primes, refactorable number, self number, Harshad number

469

469 = 7 × 67, centered hexagonal number

470s

470

470 = 2 × 5 × 47, sphenic number, nontotient, noncototient
471 = 3 × 157, sum of three consecutive primes, perfect totient number

472

472 = 23 × 59, nontotient, untouchable number, refactorable number

473

473 = 11 × 43, sum of five consecutive primes

474

474 = 2 × 3 × 79, sphenic number, sum of eight consecutive primes, nontotient, noncototient, sum of totient function for first 39 integers, untouchable number, nonagonal number

475

475 = 52 × 19, 49-gonal number, member of the Mian–Chowla sequence.

476

476 = 22 × 7 × 17, Harshad number

477

477 = 32 × 53, pentagonal number

478

478 = 2 × 239

479

A prime number, safe prime, sum of nine consecutive primes, Chen prime, Eisenstein prime with no imaginary part, self number

480

480 = 25 × 3 × 5, sum of a twin prime, sum of four consecutive primes, highly totient number, refactorable number, Harshad number

481

481 = 13 × 37, octagonal number, centered square number, Harshad number

482

482 = 2 × 241, nontotient, noncototient

483

483 = 3 × 7 × 23, sphenic number, Smith number

484

484 = 22 × 112 = 222, nontotient

485

485 = 5 × 97
486 = 2 × 35, Harshad number, Perrin number
A prime number, sum of three consecutive primes, Chen prime,
488 = 23 × 61, nontotient, refactorable number

489

489 = 3 × 163, octahedral number

490s

490

490 = 2 × 5 × 72, noncototient, sum of totient function for first 40 integers, partition number, self number.
A prime number, Sophie Germain prime, Chen prime, Eisenstein prime with no imaginary part, strictly non-palindromic number

492

492 = 22 × 3 × 41, sum of six consecutive primes, refactorable number, member of a Ruth–Aaron pair with 493 under first definition

493

493 = 17 × 29, sum of seven consecutive primes, member of a Ruth–Aaron pair with 492 under first definition

494

494 = 2 × 13 × 19, sphenic number, nontotient

495

496

496 is the third perfect number, a number whose divisors add up to the actual number.

497

497 = 7 × 71, sum of five consecutive primes

498

498 = 2 × 3 × 83, sphenic number, untouchable number, admirable number, abundant number

499

A prime number, Chen prime