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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,16

LINKS

Table of n, a(n) for n=1..100.

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

CROSSREFS

Cf. A018252, A033273, A038548, A063962, A069288, A069291, A333749, A333750, A333751.

Sequence in context: A081117 A129252 A327936 * A022929 A307706 A161102

Adjacent sequences:  A333745 A333746 A333747 * A333749 A333750 A333751

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Apr 03 2020

STATUS

approved

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Last modified November 29 04:33 EST 2021. Contains 349416 sequences. (Running on oeis4.)