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A348953
a(n) = -Sum_{d|n, d < sqrt(n)} (-1)^(d + n/d) * d.
4
0, 1, -1, 1, -1, 3, -1, -1, -1, 3, -1, 2, -1, 3, -4, -1, -1, 6, -1, 3, -4, 3, -1, -2, -1, 3, -4, 3, -1, 11, -1, -5, -4, 3, -6, 6, -1, 3, -4, 0, -1, 12, -1, 3, -9, 3, -1, -8, -1, 8, -4, 3, -1, 12, -6, 2, -4, 3, -1, 5, -1, 3, -11, -5, -6, 12, -1, 3, -4, 15, -1, 0, -1, 3, -9, 3, -8, 12, -1, -8
OFFSET
1,6
LINKS
FORMULA
G.f.: Sum_{k>=1} k * x^(k*(k + 1)) / (1 + x^k).
MATHEMATICA
Table[-DivisorSum[n, (-1)^(# + n/#) # &, # < Sqrt[n] &], {n, 1, 80}]
nmax = 80; CoefficientList[Series[Sum[k x^(k (k + 1))/(1 + x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
PROG
(PARI) A348953(n) = -sumdiv(n, d, if((d*d)<n, d*(-1)^(d + (n/d)), 0)); \\ Antti Karttunen, Nov 05 2021
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Nov 04 2021
STATUS
approved