A176654 Numbers k such that both semiprime(k)/p and semiprime(semiprime(k))/p are prime for some prime p.

1, 2, 4, 5, 6, 8, 14, 20, 21, 22, 24, 27, 28, 42, 43, 47, 52, 58, 62, 64, 65, 66, 70, 73, 75, 82, 87, 92, 97, 105, 109, 111, 116, 129, 130, 133, 135, 147, 149, 150, 161, 170, 171, 172, 189, 191, 195, 208, 220, 222, 224, 227, 241, 246, 267, 274, 276, 277, 281, 287

Offset: 1

Author

Juri-Stepan Gerasimov, Apr 22 2010

Keywords

• nonn

Comments

Indices n such that A001358(n) and A091022(n) share at least one prime factor. - R. J. Mathar, Apr 26 2010

Examples

			1 is a term because both semiprime(1)/2 = 4/2 = 2 and semiprime(semiprime(1))/2 = 10/2 = 5 are prime;
2 is a term because both semiprime(2)/3 = 6/3 = 2 and semiprime(semiprime(2))/3 = 15/3 = 5 are prime;
4 is a term because both semiprime(4)/2 = 10/2 = 5 and semiprime(semiprime(4))/2 = 26/2 = 13 are prime.
		

Crossrefs

Cf. A001358, A091022.

Programs

Maple

A091022 := proc(n) A001358(A001358(n)) ; end proc: seq(A091022(n),n=1..20) ; isA176654 := proc(n) pfsn := convert(numtheory[factorset]( A001358(n) ),list) ; pfsn1 := convert(numtheory[factorset]( A091022(n) ),list) ; op(1,pfsn) = op(1,pfsn1) or op(1,pfsn) = op(-1,pfsn1) or op(-1,pfsn) = op(1,pfsn1) or op(-1,pfsn) = op(-1,pfsn1) ; end proc: for n from 1 to 1600 do if isA176654(n) then printf("%d,",n) ; end if; end do: # R. J. Mathar, Apr 26 2010

Extensions

Most values after a(6) replaced by R. J. Mathar, Apr 26 2010