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A333748
Number of nonprime divisors of n that are <= sqrt(n).
3
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 3, 1, 1, 1, 3, 1, 2, 1, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 2, 1, 3, 2, 1, 1, 3, 1, 1, 1, 3, 1, 3, 1, 2, 1, 1, 1, 4, 1, 1, 2, 3
OFFSET
1,16
FORMULA
G.f.: Sum_{k>=1} x^(A018252(k)^2) / (1 - x^A018252(k)).
MATHEMATICA
Table[DivisorSum[n, 1 &, # <= Sqrt[n] && !PrimeQ[#] &], {n, 1, 100}]
nmax = 100; CoefficientList[Series[Sum[Boole[!PrimeQ[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) && !isprime(d)); \\ Michel Marcus, Apr 03 2020
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 03 2020
STATUS
approved