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

0,1

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).

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).

Mathematica

Total[#^Range[0, 20] & /@ Divisors[28]] (* or *) Table[(4^n + 2^n + 1) (7^n + 1), {n, 0, 20}]

Prog

(Magma) [DivisorSigma(n, 28): n in [0..20]];
(Magma) [(4^n+2^n+1)*(7^n+1): n in [0..20]];

Crossrefs

Cf. A018254 (divisors of 28).

Cf. similar sequence listed in A241029.

Sequence in context: A052317 A185524 A122743 * A268760 A137032 A053421

Adjacent sequences: A241028 A241029 A241030 * A241032 A241033 A241034

Keyword

nonn,easy,changed

Author

Vincenzo Librandi, Apr 17 2014

Status

approved