

A284927


a(n) = Sum_{dn} (1)^(n/d+1)*d^6.


8



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

1,2


COMMENTS

Multiplicative because this sequence is the Dirichlet convolution of A001014 and A062157 which are both multiplicative.  Andrew Howroyd, Jul 20 2018


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), 162 (see p. 4 and p. 8).
Index entries for sequences mentioned by Glaisher


FORMULA

G.f.: Sum_{k>=1} k^6*x^k/(1 + x^k).  Ilya Gutkovskiy, Apr 07 2017


MATHEMATICA

Table[Sum[(1)^(n/d + 1)*d^6, {d, Divisors[n]}], {n, 50}] (* Indranil Ghosh, Apr 06 2017 *)


PROG

(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


CROSSREFS

Sum_{dn} (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


KEYWORD

nonn,mult,changed


AUTHOR

Seiichi Manyama, Apr 06 2017


EXTENSIONS

Keyword:mult added by Andrew Howroyd, Jul 23 2018


STATUS

approved



