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

1,2

Comments

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

Links

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

Lucas A. Brown, Python program.

Eric Weisstein's World of Mathematics, Centered Triangular Number

Index entries for sequences related to divisors of numbers

Example

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

Prog

(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

Crossrefs

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

Sequence in context: A120599 A012797 A342907 * A167002 A227005 A054465

Adjacent sequences: A358541 A358542 A358543 * A358545 A358546 A358547

Keyword

nonn,more

Author

Ilya Gutkovskiy, Nov 21 2022

Extensions

a(14) from Michel Marcus, Nov 21 2022

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

Status

approved