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A321808 a(n) = Sum_{d divides n} (-1)^(d + n/d) * d^11. 4
1, -2049, 177148, -4192257, 48828126, -362976252, 1977326744, -8585738241, 31381236757, -100048830174, 285311670612, -742649943036, 1792160394038, -4051542498456, 8649804864648, -17583591913473, 34271896307634, -64300154115093 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
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).
FORMULA
G.f.: Sum_{k>=1} (-1)^(k+1)*k^11*x^k/(1 + x^k). - Ilya Gutkovskiy, Dec 22 2018
Multiplicative with a(2^e) = -3*(341*2^(11*e+1) + 1365)/2047, and a(p^e) = (p^(11*e+11) - 1)/(p^11 - 1) for p > 2. - Amiram Eldar, Nov 22 2022
MATHEMATICA
a[n_] := DivisorSum[n, (-1)^(# + n/#)*#^11 &]; Array[a, 50] (* Amiram Eldar, Nov 22 2022 *)
PROG
(PARI) apply( A321808(n)=sumdiv(n, d, (-1)^(n\d-d)*d^11), [1..30]) \\ M. F. Hasler, Nov 26 2018
CROSSREFS
Column k=11 of A322083.
Cf. A321543 - A321565, A321807 - A321836 for similar sequences.
Sequence in context: A071116 A060949 A230189 * A017685 A013959 A036089
KEYWORD
sign,mult
AUTHOR
N. J. A. Sloane, Nov 23 2018
STATUS
approved

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Last modified March 29 06:15 EDT 2024. Contains 371265 sequences. (Running on oeis4.)