A144775 Define f(n) = 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, 1, 2, 0, 4, 0, 6, 3, 2, 0, 10, 0, 12, 0, 0, 4, 16, 8, 18, 0, 0, 0, 22, 13, 7, 0, 2, 0, 28, 0, 30, 5, 0, 0, 0, 16, 36, 0, 0, 24, 40, 0, 42, 0, 21, 0, 46, 16, 13, 15, 0, 0, 52, 11, 0, 35, 0, 0, 58, 0, 60, 0, 31, 5, 0, 0, 66, 0, 0, 0, 70, 20, 72, 0, 27, 0, 0, 0, 78, 32, 2, 0, 82, 0, 0, 0, 0, 55

Offset

1,3

Comments

This sequence obtains a new maximum a(n) = n - 1 for prime n.

a(n) = 0 often, but not always, when n - 1 and n + 1 are twin primes.

Links

Table of n, a(n) for n=1..88.

Example

f(8) = 2 * rad(8) = 4. f(k) < 4 for 1, 2 and 3 (f(k) = k for 0 < k < 8); a(8) = 3.

Crossrefs

Cf. A000040, A001097, A007947, A144100, A144774

Sequence in context: A237420 A130891 A091371 * A249744 A245075 A046666

Adjacent sequences: A144772 A144773 A144774 * A144776 A144777 A144778

Keyword

easy,nonn

Author

Reikku Kulon, Sep 21 2008

Status

approved