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A369100 Dirichlet g.f.: zeta(s)^3 * (1 - 2^(1-s))^2. 0
1, -1, 3, -2, 3, -3, 3, -2, 6, -3, 3, -6, 3, -3, 9, -1, 3, -6, 3, -6, 9, -3, 3, -6, 6, -3, 10, -6, 3, -9, 3, 1, 9, -3, 9, -12, 3, -3, 9, -6, 3, -9, 3, -6, 18, -3, 3, -3, 6, -6, 9, -6, 3, -10, 9, -6, 9, -3, 3, -18, 3, -3, 18, 4, 9, -9, 3, -6, 9, -9, 3, -12, 3, -3, 18 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
FORMULA
Sum_{k=1..n} a(k) ~ n * log(2)^2.
Multiplicative with a(2^e) = (e^2-5*e+2)/2, and a(p^e) = (e+1)*(e+2)/2 for an odd prime p. - Amiram Eldar, Jan 13 2024
MATHEMATICA
Table[Sum[Sum[-(-1)^d, {d, Divisors[k]}]*(-1)^(n/k+1), {k, Divisors[n]}], {n, 1, 100}]
f[p_, e_] := (e + 1)*(e + 2)/2; f[2, e_] := (e^2 - 5*e + 2)/2; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Jan 13 2024 *)
PROG
(PARI) a(n) = {my(f = factor(n), p, e); prod(i = 1, #f~, p = f[i, 1]; e=f[i, 2]; if(p == 2, (e^2-5*e+2)/2, (e+1)*(e+2)/2)); } \\ Amiram Eldar, Jan 13 2024
CROSSREFS
Sequence in context: A016459 A242309 A275663 * A060585 A114451 A142246
KEYWORD
sign,mult
AUTHOR
Vaclav Kotesovec, Jan 13 2024
STATUS
approved

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Last modified May 19 00:35 EDT 2024. Contains 372666 sequences. (Running on oeis4.)