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A358542
a(n) is the smallest number with exactly n divisors that are tetrahedral numbers.
4
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
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
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