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

1, 5, 30, 140, 420, 1540, 4620, 13860, 78540, 157080, 471240, 1141140, 3603600, 3423420, 13693680, 30630600, 58198140, 116396280, 214414200, 428828400, 581981400, 1163962800, 5354228880, 4073869800, 8147739600, 26771144400, 36082846800, 80313433200, 93699005400, 187398010800

Offset: 1

Author

Ilya Gutkovskiy, Nov 21 2022

Keywords

• nonn

Comments

Any terms for n > 25 exceed 10^10. - Lucas A. Brown, Dec 24 2022

a(25) <= 8147739600, a(26) <= 26771144400, a(27) <= 36082846800, a(28) <= 80313433200. - Jon E. Schoenfield, Dec 16 2022

Examples

			a(3) = 30 because 30 has 3 square pyramidal divisors {1, 5, 30} and this is the smallest such number.
		

Links

• Lucas A. Brown, Python program.
• Eric Weisstein's World of Mathematics, Square Pyramidal Number.
• Index entries for sequences related to divisors of numbers

Crossrefs

Cf. A000330, A005179, A130279, A279496, A358542, A358545.

Programs

PARI

issqpyr(n) = my(m = sqrtnint(3*n, 3)); n==m*(m+1)*(2*m+1)/6; \\ A253903
a(n) = my(k=1); while (sumdiv(k, d, issqpyr(d)) != n, k++); k; \\ Michel Marcus, Nov 21 2022

Extensions

a(15) from Michel Marcus, Nov 21 2022

a(16)-a(20) from Jinyuan Wang, Nov 28 2022

a(21)-a(22) from Lucas A. Brown, Dec 14 2022

a(23)-a(24) from Lucas A. Brown, Dec 18 2022

a(25) from Lucas A. Brown, Dec 22 2022

a(26)-a(30) from Bert Dobbelaere, May 18 2025