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 A176654 Numbers k such that both semiprime(k)/p and semiprime(semiprime(k))/p are prime for some prime p. 1

%I #8 Feb 07 2019 02:14:21

%S 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,

%T 82,87,92,97,105,109,111,116,129,130,133,135,147,149,150,161,170,171,

%U 172,189,191,195,208,220,222,224,227,241,246,267,274,276,277,281,287

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

%C Indices n such that A001358(n) and A091022(n) share at least one prime factor. - _R. J. Mathar_, Apr 26 2010

%e 1 is a term because both semiprime(1)/2 = 4/2 = 2 and semiprime(semiprime(1))/2 = 10/2 = 5 are prime;

%e 2 is a term because both semiprime(2)/3 = 6/3 = 2 and semiprime(semiprime(2))/3 = 15/3 = 5 are prime;

%e 4 is a term because both semiprime(4)/2 = 10/2 = 5 and semiprime(semiprime(4))/2 = 26/2 = 13 are prime.

%p 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

%Y Cf. A001358, A091022.

%K nonn

%O 1,2

%A _Juri-Stepan Gerasimov_, Apr 22 2010

%E Most values after a(6) replaced by _R. J. Mathar_, Apr 26 2010

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Last modified October 3 16:02 EDT 2023. Contains 365868 sequences. (Running on oeis4.)