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%I #30 Dec 24 2022 22:28:59
%S 1,4,56,20,120,280,560,840,1680,10920,9240,18480,55440,120120,240240,
%T 314160,628320,1441440,2282280,7225680,4564560,9129120,13693680,
%U 27387360,54774720,68468400,77597520,136936800,155195040,310390080,465585120,775975200,1163962800
%N a(n) is the smallest number with exactly n divisors that are tetrahedral numbers.
%H Lucas A. Brown, <a href="/A358542/b358542.txt">Table of n, a(n) for n = 1..37</a>
%H Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/figuratedivisors.py">Python program</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TetrahedralNumber.html">Tetrahedral Number</a>
%H <a href="/index/Di#divisors">Index entries for sequences related to divisors of numbers</a>
%e a(3) = 56 because 56 has 3 tetrahedral divisors {1, 4, 56} and this is the smallest such number.
%o (PARI) istetrah(n) = my(k=sqrtnint(6*n, 3)); k*(k+1)*(k+2)==6*n; \\ A000292
%o a(n) = my(k=1); while (sumdiv(k, d, istetrah(d)) != n, k++); k; \\ _Michel Marcus_, Nov 21 2022
%Y Cf. A000292, A005179, A130317, A279495, A358543, A358544.
%K nonn
%O 1,2
%A _Ilya Gutkovskiy_, Nov 21 2022
%E a(20)-a(22) from _Michel Marcus_, Nov 21 2022
%E a(23)-a(30) from _Jinyuan Wang_, Nov 28 2022
%E a(31) from _Martin Ehrenstein_, Dec 02 2022
%E a(32) and a(33) from _Lucas A. Brown_, Dec 14 2022