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A321807
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a(n) = Sum_{d divides n} (-1)^(d + n/d) * d^10.
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55
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1, -1025, 59050, -1047553, 9765626, -60526250, 282475250, -1072692225, 3486843451, -10009766650, 25937424602, -61858004650, 137858491850, -289537131250, 576660215300, -1098436836353, 2015993900450, -3574014537275, 6131066257802
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OFFSET
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1,2
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LINKS
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FORMULA
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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
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MATHEMATICA
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a[n_] := DivisorSum[n, (-1)^(# + n/#)*#^10 &]; Array[a, 50] (* Amiram Eldar, Nov 22 2022 *)
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PROG
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(PARI) apply( A321807(n)=sumdiv(n, d, (-1)^(d-n\d)*d^10), [1..30]) \\ M. F. Hasler, Nov 26 2018
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CROSSREFS
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KEYWORD
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sign,mult
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AUTHOR
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STATUS
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approved
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