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A327124
Expansion of Sum_{k>=1} ((1 - (-x)^k)^k - 1).
3
1, -2, 3, -3, 5, -3, 7, -2, 10, 0, 11, -1, 13, 7, 25, 13, 17, -2, 19, 30, 56, 33, 23, 1, 26, 52, 111, 98, 29, -51, 31, 158, 198, 102, 56, 24, 37, 133, 325, 304, 41, -189, 43, 517, 626, 207, 47, 191, 50, -2, 731, 988, 53, -435, 517, 1315, 1026, 348, 59, 18
OFFSET
1,2
LINKS
FORMULA
a(n) = Sum_{d|n} (-1)^(n-d) * binomial(n/d,d).
a(p) = p, where p is odd prime.
MATHEMATICA
nmax = 60; CoefficientList[Series[Sum[((1 - (-x)^k)^k - 1), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
Table[DivisorSum[n, (-1)^(n - #) Binomial[n/#, #] &], {n, 1, 60}]
PROG
(PARI) a(n)={sumdiv(n, d, (-1)^(n-d) * binomial(n/d, d))} \\ Andrew Howroyd, Sep 14 2019
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Sep 14 2019
STATUS
approved