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

1,2

Comments

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

Links

Table of n, a(n) for n=1..60.

Example

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.

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

Crossrefs

Cf. A001358, A091022.

Sequence in context: A303909 A110277 A325680 * A185867 A326910 A326905

Adjacent sequences: A176651 A176652 A176653 * A176655 A176656 A176657

Keyword

nonn

Author

Juri-Stepan Gerasimov, Apr 22 2010

Extensions

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

Status

approved