A241031 Sum of n-th powers of divisors of 28.
6, 56, 1050, 25112, 655746, 17766056, 489541650, 13599182072, 379283617986, 10599157616456, 296486304875250, 8297561014164632, 232274972859656226, 6502905234227329256, 182070232515259616850, 5097810928082584052792
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (56,-1043,8240,-29204,43904,-21952).
Programs
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Magma
[DivisorSigma(n, 28): n in [0..20]];
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Magma
[(4^n+2^n+1)*(7^n+1): n in [0..20]];
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Mathematica
Total[#^Range[0, 20] & /@ Divisors[28]] (* or *) Table[(4^n + 2^n + 1) (7^n + 1), {n, 0, 20}]
Formula
G.f.: 2*(3 - 140*x + 2086*x^2 - 12360*x^3 + 29204*x^4 - 21952*x^5)/((1 - x)*(1 - 2*x)*(1 - 4*x)*(1 - 7*x)*(1 - 14*x)*(1 - 28*x)).
a(n) = (4^n + 2^n + 1)*(7^n + 1).