A358542 a(n) is the smallest number with exactly n divisors that are tetrahedral numbers.

1, 4, 56, 20, 120, 280, 560, 840, 1680, 10920, 9240, 18480, 55440, 120120, 240240, 314160, 628320, 1441440, 2282280, 7225680, 4564560, 9129120, 13693680, 27387360, 54774720, 68468400, 77597520, 136936800, 155195040, 310390080, 465585120, 775975200, 1163962800

Offset

1,2

Links

Lucas A. Brown, Table of n, a(n) for n = 1..37

Lucas A. Brown, Python program.

Eric Weisstein's World of Mathematics, Tetrahedral Number

Index entries for sequences related to divisors of numbers

Example

a(3) = 56 because 56 has 3 tetrahedral divisors {1, 4, 56} and this is the smallest such number.

Prog

(PARI) istetrah(n) = my(k=sqrtnint(6*n, 3)); k*(k+1)*(k+2)==6*n; \\ A000292
a(n) = my(k=1); while (sumdiv(k, d, istetrah(d)) != n, k++); k; \\ Michel Marcus, Nov 21 2022

Crossrefs

Cf. A000292, A005179, A130317, A279495, A358543, A358544.

Sequence in context: A355073 A054751 A189873 * A359656 A329459 A143650

Adjacent sequences: A358539 A358540 A358541 * A358543 A358544 A358545

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 21 2022

Extensions

a(20)-a(22) from Michel Marcus, Nov 21 2022

a(23)-a(30) from Jinyuan Wang, Nov 28 2022

a(31) from Martin Ehrenstein, Dec 02 2022

a(32) and a(33) from Lucas A. Brown, Dec 14 2022

Status

approved