A020516 Sum of n-th powers of divisors of 64.

7, 127, 5461, 299593, 17895697, 1108378657, 69810262081, 4432676798593, 282578800148737, 18049651735527937, 1154048505100108801, 73823022692637345793, 4723519685917965029377, 302268352895954163081217

Offset: 0

Author

Simon Plouffe

Keywords

• nonn
• easy

Comments

7th cyclotomic polynomial evaluated at powers of 2.

Links

• T. D. Noe, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A022166, A022189.

Programs

Magma

[&+[Divisors(64)[i]^n: i in [1..7]]: n in [0..15]]; // Vincenzo Librandi, Apr 17 2014

Maple

with(numtheory,cyclotomic):seq(cyclotomic(7,2^i),i=0..24);

Mathematica

Total[#^Range[0,15]&/@Divisors[64]]  (* Harvey P. Dale, Mar 21 2011 *)

PARI

a(n) = polcyclo(7, 2^n); \\ Michel Marcus, Nov 13 2016

Formula

G.f.: (-7+762 x-26670 x^2+377952 x^3-2267712 x^4+5462016 x^5-4161536 x^6)/(-1+127 x-5334 x^2+94488 x^3-755904 x^4+2731008 x^5-4161536 x^6+2097152 x^7). - Harvey P. Dale, Mar 21 2011

a(n) = (2^(7*n) - 1)/( 2^n - 1). Exp( Sum_{n >= 1} a(n)*x^n/n ) = 1 + 127*x + 10795*x^2 + ... is the o.g.f. for the 6th subdiagonal of triangle A022166, essentially A022189. - Peter Bala, Apr 07 2015