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A321807
a(n) = Sum_{d divides n} (-1)^(d + n/d) * d^10.
55
1, -1025, 59050, -1047553, 9765626, -60526250, 282475250, -1072692225, 3486843451, -10009766650, 25937424602, -61858004650, 137858491850, -289537131250, 576660215300, -1098436836353, 2015993900450, -3574014537275, 6131066257802
OFFSET
1,2
FORMULA
G.f.: Sum_{k>=1} (-1)^(k+1)*k^10*x^k/(1 + x^k). - Ilya Gutkovskiy, Dec 22 2018
Multiplicative with a(2^e) = -(511*2^(10*e+1) + 2047)/1023, and a(p^e) = (p^(10*e+10) - 1)/(p^10 - 1) for p > 2. - Amiram Eldar, Nov 22 2022
MATHEMATICA
a[n_] := DivisorSum[n, (-1)^(# + n/#)*#^10 &]; Array[a, 50] (* Amiram Eldar, Nov 22 2022 *)
PROG
(PARI) apply( A321807(n)=sumdiv(n, d, (-1)^(d-n\d)*d^10), [1..30]) \\ M. F. Hasler, Nov 26 2018
CROSSREFS
Column k=10 of A322083.
Cf. A321543 - A321565, A321808 - A321836 for similar sequences.
Sequence in context: A031742 A353943 A351273 * A351305 A017683 A013958
KEYWORD
sign,mult
AUTHOR
N. J. A. Sloane, Nov 23 2018
STATUS
approved