A144775 -id:A144775 - cp's OEIS frontend

A144776 Define f(n) = 1 if n is prime, 2 * rad(n) if four divides n and rad(n) otherwise: then a(n) = 0 for composite n where f(n) is not less than n and otherwise equals the number of positive integers k less than n for which f(k) < f(n).

0, 0, 0, 0, 0, 0, 0, 5, 5, 0, 0, 0, 0, 0, 0, 8, 0, 12, 0, 0, 0, 0, 0, 17, 14, 0, 10, 0, 0, 0, 0, 14, 0, 0, 0, 22, 0, 0, 0, 28, 0, 0, 0, 0, 29, 0, 0, 26, 25, 26, 0, 0, 0, 24, 0, 42, 0, 0, 0, 0, 0, 0, 41, 21, 0, 0, 0, 0, 0, 0, 0, 35, 0, 0, 42, 0, 0, 0, 0, 46, 23, 0, 0, 0, 0, 0, 0, 64, 0, 58, 0, 0, 0, 0, 0

Offset: 1

Reikku Kulon, Sep 21 2008

For the given terms, nearly all n for which a(n) obtains a new maximum are multiples of eight. Only 18, 36 and 45 are not.

			f(8) = 4 and f(9) = 3. For 1, 2, 3, 5 and 7, f(k) = 1, so a(8) = a(9) = 5.

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

Cf. A000040, A001097, A007947, A144100, A144774, A144775

A007947(n) = factorback(factorint(n)[, 1]);
f(n) = if(isprime(n),1,if(n%4,A007947(n),2*A007947(n)));
A144776(n) = if(n<2,0,my(x=f(n)); if(!isprime(n)&&(x>=n),0,sum(k=1,n-1,(f(k)Antti Karttunen, Jul 03 2018

cp's OEIS Frontend

A144776 Define f(n) = 1 if n is prime, 2 * rad(n) if four divides n and rad(n) otherwise: then a(n) = 0 for composite n where f(n) is not less than n and otherwise equals the number of positive integers k less than n for which f(k) < f(n).

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