A358859 a(n) is the smallest n-gonal number divisible by exactly n n-gonal numbers.

6, 36, 210, 4560, 6426, 326040, 4232250, 1969110, 296676380, 4798080, 166289760, 73765692000, 712750500, 50561280, 33944067893736, 2139168754800, 4292572951800, 1414764341760, 72461756727360, 180975331456920, 1870768457500800, 5498331930000, 153698278734000

Offset: 3

Author

Ilya Gutkovskiy, Dec 03 2022

Keywords

• nonn

Comments

The corresponding indices of n-gonal numbers are 3, 6, 12, 48, 51, 330, 1100, 702, ...

Examples

			a(5) = 210, because 210 is a pentagonal number that has 5 pentagonal divisors {1, 5, 35, 70, 210} and this is the smallest such number.
		

Links

• Eric Weisstein's World of Mathematics, Polygonal Number
• Index entries for sequences related to divisors of numbers

Crossrefs

Cf. A005179, A076983, A358539, A358860, A358861.

Programs

PARI

a(n) = if(n<3, return()); for(k=1, oo, my(t=(k*(n*k - n - 2*k + 4))\2); if(sumdiv(t, d, ispolygonal(d, n)) == n, return(t))); \\ Daniel Suteu, Dec 04 2022

Extensions

a(11)-a(25) from Daniel Suteu, Dec 04 2022