OFFSET
1,12
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
FORMULA
G.f.: Sum_{p prime, k>=1} x^(p^(2*k)) / (1 - x^(p^k)).
MAPLE
f:= proc(n) local p;
add(min(padic:-ordp(n, p), floor(1/2*log[p](n))), p=numtheory:-factorset(n))
end proc:
map(f, [$1..200]); # Robert Israel, Apr 22 2020
MATHEMATICA
Table[DivisorSum[n, 1 &, # <= Sqrt[n] && PrimePowerQ[#] &], {n, 1, 100}]
nmax = 100; CoefficientList[Series[Sum[Boole[PrimePowerQ[k]] x^(k^2)/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
PROG
(PARI) a(n) = sumdiv(n, d, (d^2<=n) && isprimepower(d)); \\ Michel Marcus, Apr 03 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 03 2020
STATUS
approved