A358545 a(n) is the smallest number with exactly n divisors that are centered square numbers.

1, 5, 25, 325, 1625, 1105, 5525, 27625, 160225, 1022125, 801125, 5928325, 8491925, 29641625, 42459625, 444215525, 314201225, 2003613625, 1571006125, 14826740825, 12882250225, 127081657625, 64411251125, 88717383625

Offset: 1

Author

Ilya Gutkovskiy, Nov 21 2022

Keywords

• nonn
• more

Comments

Any subsequent terms are > 10^10. - Lucas A. Brown, Dec 24 2022

Examples

			a(3) = 25 because 25 has 3 centered square divisors {1, 5, 25} and this is the smallest such number.
		

Links

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

Crossrefs

Cf. A001844, A005179, A130279, A300410, A358543, A358544.

Programs

PARI

iscsq(n) = issquare(2*n-1); \\ A001844
a(n) = my(k=1); while (sumdiv(k, d, iscsq(d)) != n, k++); k; \\ Michel Marcus, Nov 21 2022

Extensions

a(12)-a(15) from Michel Marcus, Nov 21 2022

a(16) from Martin Ehrenstein, Dec 02 2022

a(17)-a(24) from Jinyuan Wang, Dec 02 2022