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A358543 a(n) is the smallest number with exactly n divisors that are square pyramidal numbers.

%I A358543 #56 May 18 2025 18:50:45
%S A358543 1,5,30,140,420,1540,4620,13860,78540,157080,471240,1141140,3603600,
%T A358543 3423420,13693680,30630600,58198140,116396280,214414200,428828400,
%U A358543 581981400,1163962800,5354228880,4073869800,8147739600,26771144400,36082846800,80313433200,93699005400,187398010800
%N A358543 a(n) is the smallest number with exactly n divisors that are square pyramidal numbers.
%C A358543 Any terms for n > 25 exceed 10^10. - _Lucas A. Brown_, Dec 24 2022
%C A358543 a(25) <= 8147739600, a(26) <= 26771144400, a(27) <= 36082846800, a(28) <= 80313433200. - _Jon E. Schoenfield_, Dec 16 2022
%H A358543 Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/figuratedivisors.py">Python program</a>.
%H A358543 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SquarePyramidalNumber.html">Square Pyramidal Number</a>.
%H A358543 <a href="/index/Di#divisors">Index entries for sequences related to divisors of numbers</a>
%e A358543 a(3) = 30 because 30 has 3 square pyramidal divisors {1, 5, 30} and this is the smallest such number.
%o A358543 (PARI) issqpyr(n) = my(m = sqrtnint(3*n, 3)); n==m*(m+1)*(2*m+1)/6; \\ A253903
%o A358543 a(n) = my(k=1); while (sumdiv(k, d, issqpyr(d)) != n, k++); k; \\ _Michel Marcus_, Nov 21 2022
%Y A358543 Cf. A000330, A005179, A130279, A279496, A358542, A358545.
%K A358543 nonn
%O A358543 1,2
%A A358543 _Ilya Gutkovskiy_, Nov 21 2022
%E A358543 a(15) from _Michel Marcus_, Nov 21 2022
%E A358543 a(16)-a(20) from _Jinyuan Wang_, Nov 28 2022
%E A358543 a(21)-a(22) from _Lucas A. Brown_, Dec 14 2022
%E A358543 a(23)-a(24) from _Lucas A. Brown_, Dec 18 2022
%E A358543 a(25) from _Lucas A. Brown_, Dec 22 2022
%E A358543 a(26)-a(30) from _Bert Dobbelaere_, May 18 2025