OFFSET
1,2
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
Multiplicative with a(p^e) = p + 1 if e is odd and 1 otherwise.
a(n) >= 1, with equality if and only if n is a square (A000290).
Dirichlet g.f.: zeta(2*s) * Product_{p prime} (1 + 1/p^(s-1) + 1/p^s).
Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = zeta(4)/zeta(3) = 0.900392677639... .
MATHEMATICA
f[p_, e_] := If[OddQ[e], p + 1, 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~, if(f[i, 2]%2, f[i, 1]+1, 1)); }
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Amiram Eldar, Dec 07 2023
STATUS
approved