cp's OEIS Frontend

A333750 Number of prime power divisors of n that are <= sqrt(n).

%I A333750 #10 Apr 22 2020 17:16:02
%S A333750 0,0,0,1,0,1,0,1,1,1,0,2,0,1,1,2,0,2,0,2,1,1,0,3,1,1,1,2,0,3,0,2,1,1,
%T A333750 1,3,0,1,1,3,0,2,0,2,2,1,0,3,1,2,1,2,0,2,1,3,1,1,0,4,0,1,2,3,1,2,0,2,
%U A333750 1,3,0,4,0,1,2,2,1,2,0,4,2,1,0,4,1,1,1,3,0,4,1,2,1,1,1,4,0,2,2,3
%N A333750 Number of prime power divisors of n that are <= sqrt(n).
%H A333750 Robert Israel, <a href="/A333750/b333750.txt">Table of n, a(n) for n = 1..10000</a>
%F A333750 G.f.: Sum_{p prime, k>=1} x^(p^(2*k)) / (1 - x^(p^k)).
%p A333750 f:= proc(n) local p;
%p A333750   add(min(padic:-ordp(n,p),floor(1/2*log[p](n))),p=numtheory:-factorset(n))
%p A333750 end proc:
%p A333750 map(f, [$1..200]); # _Robert Israel_, Apr 22 2020
%t A333750 Table[DivisorSum[n, 1 &, # <= Sqrt[n] && PrimePowerQ[#] &], {n, 1, 100}]
%t A333750 nmax = 100; CoefficientList[Series[Sum[Boole[PrimePowerQ[k]] x^(k^2)/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
%o A333750 (PARI) a(n) = sumdiv(n, d, (d^2<=n) && isprimepower(d)); \\ _Michel Marcus_, Apr 03 2020
%Y A333750 Cf. A001222, A038548, A063962, A069288, A069291, A073093, A246655, A333748, A333749, A333753.
%K A333750 nonn
%O A333750 1,12
%A A333750 _Ilya Gutkovskiy_, Apr 03 2020