A155087 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).

37, 71, 103, 109, 151, 157, 163, 181, 233, 257, 263, 271, 281, 307, 397, 443, 457, 509, 599, 607, 653, 677, 691, 709, 719, 797, 821, 883, 907, 971, 1033, 1049, 1051, 1063, 1069, 1091, 1093, 1097, 1109, 1181, 1277, 1279, 1327, 1361, 1367, 1399, 1429, 1447, 1453, 1489

Offset

1,1

Links

Table of n, a(n) for n=1..50.

Example

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.

Maple

with(numtheory): composites := remove(isprime, [$2..3000]):
A155087:= select(x -> isprime(x) and not isprime(bigomega(composites[x])), [$2..2000]);

Crossrefs

Cf. A000040, A002808.

Sequence in context: A119381 A138396 A335484 * A171807 A178399 A044103

Adjacent sequences: A155084 A155085 A155086 * A155088 A155089 A155090

Keyword

nonn

Author

Juri-Stepan Gerasimov, Jan 20 2009, Jan 28 2009

Extensions

Corrected and edited by D. S. McNeil, Mar 19 2009

Status

approved