OFFSET
1,4
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
FORMULA
G.f.: Sum_{p prime, k>=1} p^k * x^(p^(2*k)) / (1 - x^(p^k)).
MAPLE
f:= proc(n) local F, i, j, t;
F:= ifactors(n)[2];
t:= 0;
for i from 1 to nops(F) do
j:= min(F[i, 2], ilog[F[i, 1]^2](n));
t:= t + (F[i, 1]^j-1)*F[i, 1]/(F[i, 1]-1)
od;
t
end proc:
map(f, [$1..100]); # Robert Israel, Feb 15 2023
MATHEMATICA
Table[DivisorSum[n, # &, # <= Sqrt[n] && PrimePowerQ[#] &], {n, 1, 90}]
nmax = 90; CoefficientList[Series[Sum[Boole[PrimePowerQ[k]] k x^(k^2)/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
PROG
(PARI) a(n) = sumdiv(n, d, if ((d^2<=n) && isprimepower(d), d)); \\ Michel Marcus, Apr 03 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 03 2020
STATUS
approved