A241032 Sum of n-th powers of divisors of 30.

8, 72, 1300, 31752, 872644, 25170552, 741453700, 22051219752, 658764967684, 19722455410392, 591076720682500, 17723450167663752, 531571748759349124, 15945186209351359032, 478326193010497869700, 14349345894391097803752

Offset: 0

Author

Vincenzo Librandi, Apr 17 2014

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (72,-1942,25992,-190081,779760,-1747800,1944000,-810000).

Crossrefs

Cf. A018255 (divisors of 30).

Cf. similar sequence listed in A241029.

Programs

Magma

[DivisorSigma(n, 30): n in [0..20]];

Mathematica

Total[#^Range[0, 20] & /@ Divisors[30]]

Formula

G.f.: (8 - 504*x + 11652*x^2 - 129960*x^3 + 760324*x^4 - 2339280* x^5 + 3495600*x^6 - 1944000*x^7) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 5*x)*(1 - 6*x)*(1 - 10*x)*(1 - 15*x)*(1 - 30*x)).

a(n) = (1 + 2^n)*(1 + 3^n)*(1 + 5^n).