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A050459 a(n) = Sum_{d|n, d==1 mod 4} d^3 - Sum_{d|n, d==3 mod 4} d^3. 2
1, 1, -26, 1, 126, -26, -342, 1, 703, 126, -1330, -26, 2198, -342, -3276, 1, 4914, 703, -6858, 126, 8892, -1330, -12166, -26, 15751, 2198, -18980, -342, 24390, -3276, -29790, 1, 34580, 4914, -43092, 703, 50654, -6858, -57148, 126, 68922, 8892, -79506, -1330 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Multiplicative because it is the Inverse Möbius transform of [1 0 -3^3 0 5^3 0 -7^3 ...], which is multiplicative. - Christian G. Bower, May 18 2005

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..10000

J. W. L. Glaisher, On the representations of a number as the sum of two, four, six, eight, ten, and twelve squares, Quart. J. Math. 38 (1907), 1-62 (see p. 4 and p. 8).

Index entries for sequences mentioned by Glaisher

FORMULA

a(n) = A050451(n) - A050454(n).

G.f.: Sum_{k>=1} (-1)^(k-1)*(2*k - 1)^3*x^(2*k-1)/(1 - x^(2*k-1)). - Ilya Gutkovskiy, Dec 22 2018

MAPLE

A050459 := proc(n) local a; a := 0 ; for d in numtheory[divisors](n) do if d mod 4 = 1 then a := a+d^3 ; elif d mod 4 = 3 then a := a-d^3 ; end if; end do;  a ; end proc:

seq(A050459(n), n=1..100) ; # R. J. Mathar, Jan 07 2011

MATHEMATICA

s[n_, r_] := DivisorSum[n, #^3 &, Mod[#, 4]==r &]; a[n_] := s[n, 1] - s[n, 3]; Array[a, 30] (* Amiram Eldar, Dec 06 2018 *)

CROSSREFS

Column k=3 of A322143.

Glaisher's E_i (i=0..12): A002654, A050457, A002173, A050459, A050456, A321821, A321822, A321823, A321824, A321825, A321826, A321827, A321828

Sequence in context: A040700 A070614 A040701 * A040669 A040668 A040667

Adjacent sequences:  A050456 A050457 A050458 * A050460 A050461 A050462

KEYWORD

sign,mult

AUTHOR

N. J. A. Sloane, Dec 23 1999

STATUS

approved

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Last modified September 21 02:29 EDT 2020. Contains 337266 sequences. (Running on oeis4.)