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Primes of the form (number of prime factors of n-th composite) plus (number of divisors of n-th composite).
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%I #13 Oct 01 2020 03:36:23

%S 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,

%T 11,11,5,11,11,23,11,11,11,11,13,17,11,13,11,11,11,11,11,23,11,17,11,

%U 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

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

%C 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

%H Robert Israel, <a href="/A167133/b167133.txt">Table of n, a(n) for n = 1..10000</a>

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

%p f:= proc(n) local F,x;

%p if isprime(n) then return NULL fi;

%p F:= ifactors(n)[2];

%p x:= add(t[2],t=F) + mul(1+t[2],t=F);

%p if isprime(x) then x fi

%p end proc:

%p map(f, [$4..1000]); # _Robert Israel_, Sep 30 2020

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

%Y Cf. A035004, A062502.

%K nonn

%O 1,1

%A _Juri-Stepan Gerasimov_, Oct 28 2009

%E Corrected and extended by _R. J. Mathar_, Oct 29 2009