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

1,2

Comments

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

Links

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

Example

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.

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

Crossrefs

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

Sequence in context: A337475 A141803 A249147 * A127242 A325392 A025853

Adjacent sequences: A260645 A260646 A260647 * A260649 A260650 A260651

Keyword

nonn

Author

Gionata Neri, Nov 12 2015

Extensions

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

Status

approved