A260648 Number of distinct prime divisors p of the n-th composite number c such that gpf(c - p) = p, where gpf = greatest prime factor (A006530).

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

Offset: 1

Author

Gionata Neri, Nov 12 2015

Keywords

• nonn

Comments

a(n) gives the number of times that the n-th composite number occurs in A070229.

Examples

			a(8) = 2 since the distinct prime divisors of A002808(8) = 15 are 3 and 5, A006530(15 - 3) = 3 and A006530(15 - 5) = 5, so all prime 3 and 5 are to be considered.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002808 (composite), A006530 (gpf).

Programs

Maple

N:= 1000: # to consider composites <= N
f:= proc(c) local p, t;
   if isprime(c) then return NULL fi;
   nops(select(p -> max(numtheory:-factorset(c/p-1))<=p, numtheory:-factorset(c)))
end proc:
map(f, [$4..N]); # Robert Israel, May 02 2017

Extensions

a(87) corrected by Robert Israel, May 02 2017