A167133 Primes of the form (number of prime factors of n-th composite) plus (number of divisors of n-th composite).

5, 7, 5, 5, 7, 11, 11, 13, 11, 5, 13, 11, 11, 17, 11, 13, 11, 11, 17, 11, 11, 5, 7, 11, 11, 11, 11, 5, 11, 11, 23, 11, 11, 11, 11, 13, 17, 11, 13, 11, 11, 11, 11, 11, 23, 11, 17, 11, 11, 11, 11, 11, 11, 5, 11, 23, 11, 11, 11, 7, 11, 11, 11, 5, 11, 11, 11, 11, 17, 23, 11, 11, 11, 11

Offset

1,1

Comments

Contains every prime > 3 infinitely many times, as A000005(p^k)+A001222(p^k)=2*k+1 for prime p. - Robert Israel, Sep 30 2020

Links

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

Example

a(1) = 2+3 = 5 (for 1st composite=4); a(2) = 3+4 = 7 (for 3rd composite=8).

Maple

f:= proc(n) local F, x;
  if isprime(n) then return NULL fi;
  F:= ifactors(n)[2];
  x:= add(t[2], t=F) + mul(1+t[2], t=F);
  if isprime(x) then x fi
end proc:
map(f, [$4..1000]); # Robert Israel, Sep 30 2020

Crossrefs

Cf. A000005, A000040, A002808, A001222, A069346.

Cf. A035004, A062502.

Sequence in context: A367549 A122271 A011205 * A144567 A372204 A215732

Adjacent sequences: A167130 A167131 A167132 * A167134 A167135 A167136

Keyword

nonn

Author

Juri-Stepan Gerasimov, Oct 28 2009

Extensions

Corrected and extended by R. J. Mathar, Oct 29 2009

Status

approved