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A167133
Primes of the form (number of prime factors of n-th composite) plus (number of divisors of n-th composite).
1
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
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
KEYWORD
nonn
AUTHOR
EXTENSIONS
Corrected and extended by R. J. Mathar, Oct 29 2009
STATUS
approved