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A034665 Sum of n-th powers of divisors of 32. 4
6, 63, 1365, 37449, 1118481, 34636833, 1090785345, 34630287489, 1103823438081, 35253226045953, 1127000493261825, 36046397799139329, 1153203048319815681, 36897992296869404673, 1180663682709764194305 (list; graph; refs; listen; history; text; internal format)
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 * A218383 A222596 A067447

Adjacent sequences: A034662 A034663 A034664 * A034666 A034667 A034668

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified February 5 03:48 EST 2023. Contains 360082 sequences. (Running on oeis4.)