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A284927
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a(n) = Sum_{d|n} (-1)^(n/d+1)*d^6.
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8
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1, 63, 730, 4031, 15626, 45990, 117650, 257983, 532171, 984438, 1771562, 2942630, 4826810, 7411950, 11406980, 16510911, 24137570, 33526773, 47045882, 62988406, 85884500, 111608406, 148035890, 188327590, 244156251, 304089030, 387952660, 474247150, 594823322
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OFFSET
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1,2
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COMMENTS
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Multiplicative because this sequence is the Dirichlet convolution of A001014 and A062157 which are both multiplicative. - Andrew Howroyd, Jul 20 2018
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LINKS
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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
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FORMULA
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G.f.: Sum_{k>=1} k^6*x^k/(1 + x^k). - Ilya Gutkovskiy, Apr 07 2017
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MATHEMATICA
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Table[Sum[(-1)^(n/d + 1)*d^6, {d, Divisors[n]}], {n, 50}] (* Indranil Ghosh, Apr 06 2017 *)
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PROG
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(PARI) a(n) = sumdiv(n, d, (-1)^(n/d + 1)*d^6); \\ Indranil Ghosh, Apr 06 2017
(Python)
from sympy import divisors
print [sum([(-1)**(n/d + 1)*d**6 for d in divisors(n)]) for n in range(1, 51)] # Indranil Ghosh, Apr 06 2017
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CROSSREFS
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Sum_{d|n} (-1)^(n/d+1)*d^k: A000593 (k=1), A078306 (k=2), A078307 (k=3), A284900 (k=4), A284926 (k=5), this sequence (k=6).
Cf. A001014, A062157.
Sequence in context: A069091 A123866 A024004 * A321545 A201886 A232794
Adjacent sequences: A284924 A284925 A284926 * A284928 A284929 A284930
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KEYWORD
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nonn,mult,changed
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AUTHOR
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Seiichi Manyama, Apr 06 2017
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EXTENSIONS
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Keyword:mult added by Andrew Howroyd, Jul 23 2018
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STATUS
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approved
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