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

Offset

1,2

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

Links

Table of n, a(n) for n=1..25.

Lucas A. Brown, Python program.

Eric Weisstein's World of Mathematics, Square Pyramidal Number.

Index entries for sequences related to divisors of numbers

Example

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

Prog

(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

Crossrefs

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

Sequence in context: A227267 A213260 A054612 * A282078 A080951 A375253

Adjacent sequences: A358540 A358541 A358542 * A358544 A358545 A358546

Keyword

nonn,more

Author

Ilya Gutkovskiy, 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

Status

approved