

A321549


a(n) = Sum_{dn} (1)^(d1)*d^10.


2



1, 1023, 59050, 1049599, 9765626, 60408150, 282475250, 1074791423, 3486843451, 9990235398, 25937424602, 61978820950, 137858491850, 288972180750, 576660215300, 1100586419199, 2015993900450, 3567040850373, 6131066257802, 10249991283974, 16680163512500, 26533985367846, 41426511213650
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OFFSET

1,2


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} (1)^(k1)*k^10*x^k/(1  x^k).  Ilya Gutkovskiy, Dec 23 2018
Multiplicative with a(2^e) = 2  (2^(10*e + 10)  1)/1023, and a(p^e) = (p^(10*e + 10)  1)/(p^10  1) for p > 2.  Amiram Eldar, Nov 04 2022


MATHEMATICA

f[p_, e_] := (p^(10*e + 10)  1)/(p^10  1); f[2, e_] := 2  (2^(10*e + 10)  1)/1023; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 24] (* Amiram Eldar, Nov 04 2022 *)


PROG

(PARI) apply( a(n)=sumdiv(n, d, (1)^(d1)*d^10), [1..30]) \\ M. F. Hasler, Nov 26 2018


CROSSREFS

Cf. A321543  A321565, A321807  A321836 for similar sequences.
Sequence in context: A024008 A123867 A321555 * A160959 A022192 A069385
Adjacent sequences: A321546 A321547 A321548 * A321550 A321551 A321552


KEYWORD

sign,mult


AUTHOR

N. J. A. Sloane, Nov 23 2018


STATUS

approved



