

A176654


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


1



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
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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

JuriStepan Gerasimov, Apr 22 2010


EXTENSIONS

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


STATUS

approved



