Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #52 Jan 02 2024 02:43:44
%S 1,5,30,140,420,1540,4620,13860,78540,157080,471240,1141140,3603600,
%T 3423420,13693680,30630600,58198140,116396280,214414200,428828400,
%U 581981400,1163962800,5354228880,4073869800,8147739600
%N a(n) is the smallest number with exactly n divisors that are square pyramidal numbers.
%C Any terms for n > 25 exceed 10^10. - _Lucas A. Brown_, Dec 24 2022
%C a(25) <= 8147739600, a(26) <= 26771144400, a(27) <= 36082846800, a(28) <= 80313433200. - _Jon E. Schoenfield_, Dec 16 2022
%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/SquarePyramidalNumber.html">Square Pyramidal Number</a>.
%H <a href="/index/Di#divisors">Index entries for sequences related to divisors of numbers</a>
%e a(3) = 30 because 30 has 3 square pyramidal divisors {1, 5, 30} and this is the smallest such number.
%o (PARI) issqpyr(n) = my(m = sqrtnint(3*n, 3)); n==m*(m+1)*(2*m+1)/6; \\ A253903
%o a(n) = my(k=1); while (sumdiv(k, d, issqpyr(d)) != n, k++); k; \\ _Michel Marcus_, Nov 21 2022
%Y Cf. A000330, A005179, A130279, A279496, A358542, A358545.
%K nonn,more
%O 1,2
%A _Ilya Gutkovskiy_, Nov 21 2022
%E a(15) from _Michel Marcus_, Nov 21 2022
%E a(16)-a(20) from _Jinyuan Wang_, Nov 28 2022
%E a(21)-a(22) from _Lucas A. Brown_, Dec 14 2022
%E a(23)-a(24) from _Lucas A. Brown_, Dec 18 2022
%E a(25) from _Lucas A. Brown_, Dec 22 2022