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 A333806 Number of distinct prime divisors of n that are < sqrt(n). 35
 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 1, 1, 0, 2, 0, 1, 1, 1, 0, 2, 0, 1, 1, 1, 0, 3, 0, 1, 1, 1, 1, 2, 0, 1, 1, 2, 0, 2, 0, 1, 2, 1, 0, 2, 0, 2, 1, 1, 0, 2, 1, 2, 1, 1, 0, 3, 0, 1, 2, 1, 1, 2, 0, 1, 1, 3, 0, 2, 0, 1, 2, 1, 1, 2, 0, 2, 1, 1, 0, 3, 1, 1, 1, 1, 0, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,12 COMMENTS a(n) = 0 if and only if n = p^k where p is prime and k is 0, 1, or 2. - Charles R Greathouse IV, Apr 07 2020 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 FORMULA G.f.: Sum_{k>=1} x^(prime(k)*(prime(k) + 1)) / (1 - x^prime(k)). MAPLE N:= 100: # for a(1)..a(N) V:= Vector(N): p:= 1: do   p:= nextprime(p);   if p^2 >= N then break fi;   L:= [seq(p*k, k=p+1..N/p)];   V[L]:= V[L]+~1 od: convert(V, list); # Robert Israel, Apr 07 2020 MATHEMATICA Table[DivisorSum[n, 1 &, # < Sqrt[n] && PrimeQ[#] &], {n, 1, 90}] nmax = 90; CoefficientList[Series[Sum[x^(Prime[k] (Prime[k] + 1))/(1 - x^Prime[k]), {k, 1, nmax}], {x, 0, nmax}], x] // Rest PROG (PARI) a(n)=my(f=factor(n)[, 1]); sum(i=1, #f, f[i]^2

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Last modified May 14 13:50 EDT 2021. Contains 343884 sequences. (Running on oeis4.)