A034665 Sum of n-th powers of divisors of 32.

6, 63, 1365, 37449, 1118481, 34636833, 1090785345, 34630287489, 1103823438081, 35253226045953, 1127000493261825, 36046397799139329, 1153203048319815681, 36897992296869404673, 1180663682709764194305

Offset

0,1

Links

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

Quynh Nguyen, Jean Pedersen, and Hien T. Vu, New Integer Sequences Arising From 3-Period Folding Numbers, Vol. 19 (2016), Article 16.3.1. See Table 1.

Index entries for linear recurrences with constant coefficients, signature (63,-1302,11160,-41664,64512,-32768).

Formula

G.f.: -3*(21504*x^5-27776*x^4+11160*x^3-1736*x^2+105*x-2) / ((x-1)*(2*x-1)*(4*x-1)*(8*x-1)*(16*x-1)*(32*x-1)). - Colin Barker, Apr 20 2014

a(n) = (2^(6*n) - 1)/( 2^n - 1). Exp( Sum_{n >= 1} a(n)*x^n/n ) = 1 + 63*x + 2667*x^2 + 97155*x^3 + ... is the o.g.f. for the 5th subdiagonal of triangle A022166, essentially A006110. - Peter Bala, Apr 07 2015

a(n) = 1 + 2^n + 4^n + 8^n + 16^n + 32^n for n>=0. - Karl V. Keller, Jr., Feb 02 2021

Mathematica

Total[#^Range[0, 15]&/@Divisors[32]] (* Vincenzo Librandi, Apr 17 2014 *)
LinearRecurrence[{63, -1302, 11160, -41664, 64512, -32768}, {6, 63, 1365, 37449, 1118481, 34636833}, 20] (* Harvey P. Dale, Jan 10 2015 *)

Prog

(Sage) [sigma(32, n)for n in range(0, 15)] # Zerinvary Lajos, Jun 04 2009
(Magma) [DivisorSigma(n, 32): n in [0..15]]; // Vincenzo Librandi, Apr 17 2014
(PARI) a(n)=(64^n-1)/(2^n-1) \\ Charles R Greathouse IV, Oct 07 2015
(Python) print([1+2**n+4**n+8**n+16**n+32**n for n in range(15)]) # Karl V. Keller, Jr., Feb 02 2021

Crossrefs

Cf. A006110, A022166.

Sequence in context: A079244 A023815 A249590 * A339140 A218383 A222596

Adjacent sequences: A034662 A034663 A034664 * A034666 A034667 A034668

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved