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

Author

Ilya Gutkovskiy, Nov 21 2022

Keywords

• nonn

Examples

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

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

Crossrefs

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

Programs

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

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