OFFSET
1,2
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
Multiplicative with a(p) = p^2, a(p^e) = p if e is even, and a(p^e) = 1 is e is odd and > 1.
a(n) = A356192(n)/n.
a(n) = 1 if and only if n is in A335988.
Dirichlet g.f.: zeta(2*s) * Product_{p prime} (1 + 1/p^(3*s) - 1/p^(3*s-2) - 1/p^(2*s) + 1/p^(2*s-1) + 1/p^(s-2)).
Sum_{k=1..n} a(k) ~ c * n^3 / 3, where c = (2*Pi^4/315) * Product_{p prime} (1 - p^2 - p^3 + p^4 + p^8 + p^9)/(p^8*(p+1)) = 0.207915752545... .
MATHEMATICA
f[p_, e_] := p^If[OddQ[e], Max[e, 3] - e, 1]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
PROG
(PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i, 1]^if(f[i, 2]%2, max(f[i, 2], 3) - f[i, 2], 1))};
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Amiram Eldar, Aug 31 2023
STATUS
approved