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A050471 a(n) = sum_{d|n, n/d=1 mod 4} d^3 - sum_{d|n, n/d=3 mod 4} d^3. 5

%I

%S 1,8,26,64,126,208,342,512,703,1008,1330,1664,2198,2736,3276,4096,

%T 4914,5624,6858,8064,8892,10640,12166,13312,15751,17584,18980,21888,

%U 24390,26208,29790,32768,34580,39312,43092,44992,50654,54864,57148

%N a(n) = sum_{d|n, n/d=1 mod 4} d^3 - sum_{d|n, n/d=3 mod 4} d^3.

%C Multiplicative because it is the Dirichlet convolution of A000578 = n^3 and A101455 = [1 0 -1 0 1 0 -1 ...], which are both multiplicative. - _Christian G. Bower_, May 17 2005

%H Seiichi Manyama, <a href="/A050471/b050471.txt">Table of n, a(n) for n = 1..10000</a>

%H J. W. L. Glaisher, <a href="https://books.google.com/books?id=bLs9AQAAMAAJ&amp;pg=RA1-PA1">On the representations of a number as the sum of two, four, six, eight, ten, and twelve squares</a>, Quart. J. Math. 38 (1907), 1-62 (see p. 4 and p. 8).

%H <a href="/index/Ge#Glaisher">Index entries for sequences mentioned by Glaisher</a>

%F G.f.: Sum_{n>=1} n^3*x^n/(1+x^(2*n)). - _Vladeta Jovovic_, Oct 16 2002

%t max = 40; s = Sum[n^3*x^(n-1)/(1+x^(2*n)), {n, 1, max}] + O[x]^max; CoefficientList[s, x] (* _Jean-Fran├žois Alcover_, Dec 02 2015, after _Vladeta Jovovic_ *)

%o (PARI) a(n) = sumdiv(n, d, d^3*(((n/d) % 4)==1)) - sumdiv(n, d, d^3*(((n/d) % 4)==3)); \\ _Michel Marcus_, Feb 16 2015

%Y Cf. A050469, A050470, A050468.

%K nonn,mult

%O 1,2

%A _N. J. A. Sloane_, Dec 23 1999

%E Offset changed from 0 to 1 by _R. J. Mathar_, Jul 15 2010

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Last modified January 17 20:36 EST 2020. Contains 330987 sequences. (Running on oeis4.)