%I
%S 1,2,4,6,21,42,87,120,141,142,168,179,185,188,245,255,320,363,387,434,
%T 464,496,539,593,675,697,721,753,794,810,894,929,995,1023,1032,1060,
%U 1080,1081,1105,1147,1166,1221,1224,1228,1275,1356,1391,1477,1478,1498
%N Numbers k such that both semiprime(k)/p and semiprime(k+1)/p are prime for some prime p.
%C Indices n such that A001358(n) and A001358(n+1) share one prime factor.  _R. J. Mathar_, Apr 26 2010
%H Harvey P. Dale, <a href="/A176652/b176652.txt">Table of n, a(n) for n = 1..1000</a>
%e 2 is a term because both semiprime(2)/3 = 6/3 = 2 and semiprime(2+1)/3 = 9/3 = 3 are prime.
%p isA176652 := proc(n) pfsn := convert(numtheory[factorset]( A001358(n) ),list) ; pfsn1 := convert(numtheory[factorset]( A001358(n+1) ),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 isA176652(n) then printf("%d,",n) ; end if; end do: # _R. J. Mathar_, Apr 26 2010
%t sppQ[{a_,b_}]:=Module[{af=FactorInteger[a][[All,1]],bf=FactorInteger[b][[All, 1]]},Length[Intersection[af,bf]]==1]; Position[Partition[ Select[ Range[7000],PrimeOmega[#]==2&],2,1],_?sppQ]//Flatten (* _Harvey P. Dale_, Oct 08 2017 *)
%Y Cf. A001358.
%K nonn
%O 1,2
%A _JuriStepan Gerasimov_, Apr 22 2010
%E Extended beyond 141 by _R. J. Mathar_, Apr 26 2010
%E Name clarified by _Jon E. Schoenfield_, Feb 06 2019
