OFFSET
1,2
COMMENTS
The sum of these divisors is A107749(n).
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
Multiplicative with a(2^e) = e+1 and a(p^e) = 2 for an odd prime p.
a(n) <= A000005(n), with equality if and only if n is in A122132 (or equivalently, n is not in A038838).
Dirichlet g.f.: (4^s/(4^s-1)) * zeta(s)^2/zeta(2*s).
Sum_{k==1..n} a(k) ~ (8/Pi^2)*n*(log(n) + 2*gamma - 2*log(2)/3 - 2*zeta'(2)/zeta(2) - 1), where gamma is Euler's constant (A001620).
MATHEMATICA
f[p_, e_] := If[p == 2, e + 1, 2]; 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, 1] == 2, f[i, 2]+1, 2)); }
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Amiram Eldar, Aug 26 2023
STATUS
approved