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