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A321546
a(n) = Sum_{d|n} (-1)^(d-1)*d^7.
3
1, -127, 2188, -16511, 78126, -277876, 823544, -2113663, 4785157, -9922002, 19487172, -36126068, 62748518, -104590088, 170939688, -270549119, 410338674, -607714939, 893871740, -1289938386, 1801914272, -2474870844, 3404825448, -4624694644, 6103593751, -7969061786, 10465138360, -13597534984, 17249876310
OFFSET
1,2
FORMULA
G.f.: Sum_{k>=1} (-1)^(k-1)*k^7*x^k/(1 - x^k). - Ilya Gutkovskiy, Dec 23 2018
Multiplicative with a(2^e) = 2 - (2^(7*e + 7) - 1)/127, and a(p^e) = (p^(7*e + 7) - 1)/(p^7 - 1) for p > 2. - Amiram Eldar, Nov 04 2022
MATHEMATICA
f[p_, e_] := (p^(7*e + 7) - 1)/(p^7 - 1); f[2, e_] := 2 - (2^(7*e + 7) - 1)/127; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 30] (* Amiram Eldar, Nov 04 2022 *)
PROG
(PARI) apply( a(n)=sumdiv(n, d, (-1)^(d-1)*d^7), [1..30]) \\ M. F. Hasler, Nov 26 2018
CROSSREFS
Cf. A321543 - A321565, A321807 - A321836 for similar sequences.
Sequence in context: A024005 A258808 A321552 * A345458 A008398 A144969
KEYWORD
sign,mult
AUTHOR
N. J. A. Sloane, Nov 23 2018
STATUS
approved