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

1,8

Comments

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.

Links

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

Example

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

Prog

(PARI)
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)<x)))); \\ Antti Karttunen, Jul 03 2018

Crossrefs

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

Sequence in context: A266668 A043299 A375071 * A371264 A065937 A197738

Adjacent sequences: A144773 A144774 A144775 * A144777 A144778 A144779

Keyword

easy,nonn

Author

Reikku Kulon, Sep 21 2008

Status

approved