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A321551
a(n) = Sum_{d|n} (-1)^(d-1)*d^12.
4
1, -4095, 531442, -16781311, 244140626, -2176254990, 13841287202, -68736258047, 282430067923, -999755863470, 3138428376722, -8918293480462, 23298085122482, -56680071092190, 129746582562692, -281543712968703, 582622237229762, -1156551128144685, 2213314919066162, -4096999772640686
OFFSET
1,2
FORMULA
G.f.: Sum_{k>=1} (-1)^(k-1)*k^12*x^k/(1 - x^k). - Ilya Gutkovskiy, Dec 24 2018
Multiplicative with a(2^e) = 2 - (2^(12*e + 12) - 1)/4095, and a(p^e) = (p^(12*e + 12) - 1)/(p^12 - 1) for p > 2. - Amiram Eldar, Nov 04 2022
MATHEMATICA
f[p_, e_] := (p^(12*e + 12) - 1)/(p^12 - 1); f[2, e_] := 2 - (2^(12*e + 12) - 1)/4095; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 20] (* Amiram Eldar, Nov 04 2022 *)
PROG
(PARI) apply( a(n)=sumdiv(n, d, (-1)^(d-1)*d^12), [1..30]) \\ M. F. Hasler, Nov 26 2018
CROSSREFS
Cf. A321543 - A321565, A321807 - A321836 for similar sequences.
Sequence in context: A024010 A123868 A321557 * A161004 A022194 A069387
KEYWORD
sign,mult
AUTHOR
N. J. A. Sloane, Nov 23 2018
STATUS
approved