A117948 Sum of the divisors of pentagonal numbers.

1, 6, 28, 36, 48, 72, 144, 168, 182, 180, 372, 576, 280, 336, 864, 720, 558, 702, 1120, 1080, 1024, 1008, 1296, 2016, 1178, 1344, 3600, 2016, 1320, 2160, 2304, 3720, 2736, 1836, 4704, 4212, 2736, 2280, 5040, 6048, 2604, 4992, 5588, 4752, 5304, 3312

Offset: 1

Author

Jonathan Vos Post, Apr 04 2006

Keywords

• easy
• nonn

Examples

			a(5) = 48 because the divisors of 5*(3*5-1)/2 = 35 are 1, 5, 7 and 35, having sum 48.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203, A000326, A074285, A117949.

Programs

Maple

with(numtheory): seq(sigma(n*(3*n-1)/2),n=1..46); # Emeric Deutsch, Apr 15 2006

Mathematica

Table[DivisorSigma[1,(n(3n-1))/2],{n,50}] (* Harvey P. Dale, Jul 05 2015 *)

PARI

a(n) = sigma(n*(3*n-1)/2); \\ Amiram Eldar, Dec 14 2024

Formula

a(n) = sigma(n(3n-1)/2), where sigma is the sum of divisors function. - Emeric Deutsch, Apr 15 2006

Sum_{k=1..n} a(k) ~ (9/10) * n^3. - Amiram Eldar, Dec 14 2024

Extensions

a(0) removed by Amiram Eldar, Aug 17 2019