A262202 -id:A262202 - cp's OEIS frontend

A262262 Number of prime divisors p | n such that p^2 < n and p^2 does not divide n.

0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 3, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 2, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 2, 0, 1, 1, 0, 1, 2, 0, 0, 1, 3, 0, 0, 0, 1, 1, 0, 1, 2, 0, 1, 0, 1, 0, 2, 1, 1, 1, 0, 0, 2, 1, 0, 1, 1, 1, 1, 0

Offset: 1

Juri-Stepan Gerasimov, Sep 16 2015

a(n) = 0 if n is a prime power.
From Michael De Vlieger, Sep 17 2015: (Start)
Let k be a prime divisor p | n such that p^2 < n and d^2 does not divide n.
a(n) <= A262202(n), as any k = p^2 is a special case of a (prime or nonprime) divisor d of n where d is prime.
a(n) <= A010846(n), as any k is regular to n, i.e., k is a product less than n of the prime divisors of n.
a(n) <= A045763(n), as any k neither divides nor is coprime to n.
a(n) <= A243822(n), as any k is a "semidivisor" of n, i.e., k is a product less than n of the prime divisors of n that do not divide n.
(End)

			a(6) = 1 because 4, 9 are squares of prime divisors of 6 and only 4 < 6 does not divide 6.

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A010846, A045763, A243822, A262202.

f[n_] := Block[{d = First /@ FactorInteger@ n}, Select[d^2, And[Mod[n, #] != 0, # < n] &]]; Length@ f@ # & /@ Range@ 120 (* Michael De Vlieger, Sep 17 2015 *)

a(n) = sumdiv(n, d, isprime(d) && (d^2 < n) && (n % d^2)); \\ Michel Marcus, Sep 17 2015

a(n)=my(f=factor(n)[,1]); sum(i=1,#f,f[i]^2Charles R Greathouse IV, Sep 17 2015

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A262262 Number of prime divisors p | n such that p^2 < n and p^2 does not divide n.

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