A358544 a(n) is the smallest number with exactly n divisors that are centered triangular numbers.

1, 4, 20, 320, 460, 5440, 14260, 12920, 168640, 103360, 594320, 3878720, 2377280, 9211960, 18423920, 36847840, 125995840, 73695680, 865924240, 976467760, 1952935520, 3463696960, 3905871040, 31246968320, 22946992360

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) = 20 because 20 has 3 centered triangular divisors {1, 4, 10} and this is the smallest such number.
		

Links

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

Crossrefs

Cf. A005179, A005448, A130317, A300409, A358542, A358545.

Programs

PARI

isct(n) = my(k=(2*n-2)/3, m); (n==1) || ((denominator(k)==1) && (m=sqrtint(k)) && (m*(m+1)==k)); \\ A005448
a(n) = my(k=1); while (sumdiv(k, d, isct(d)) != n, k++); k; \\ Michel Marcus, Nov 21 2022

Extensions

a(14) from Michel Marcus, Nov 21 2022

a(15)-a(25) from Jinyuan Wang, Nov 29 2022