A155087 - OEIS

%I #4 Mar 31 2012 14:47:12

%S 37,71,103,109,151,157,163,181,233,257,263,271,281,307,397,443,457,

%T 509,599,607,653,677,691,709,719,797,821,883,907,971,1033,1049,1051,

%U 1063,1069,1091,1093,1097,1109,1181,1277,1279,1327,1361,1367,1399,1429,1447,1453,1489

%N Primes p such that Omega(c(p)) is composite, where Omega(n) is the number of prime divisors of n counted with multiplicity (A001222) and c(n) is the n-th composite number (A002808).

%e 37 is such a prime as the 37th composite number is 54 and Omega(54) = Omega(2^1*3^3) = 4, which is composite. Likewise 71, as c(71) = 96, and Omega(96) = Omega(2^5*3^1) = 6 which is composite. 113 is not such a prime, as Omega(c(113)) = Omega(148) = Omega(2^2*37^1) =3 which is prime.

%p with(numtheory): composites := remove(isprime, [$2..3000]):

%p A155087:= select(x -> isprime(x) and not isprime(bigomega(composites[x])), [$2..2000]);

%Y Cf. A000040, A002808.

%K nonn

%O 1,1

%A _Juri-Stepan Gerasimov_, Jan 20 2009, Jan 28 2009

%E Corrected and edited by _D. S. McNeil_, Mar 19 2009