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%I #18 Jul 24 2020 16:22:26
%S 5,7,8,11,16,18,19,23,25,27,28,30,34,36,39,42,43,50,53,54,56,57,60,62,
%T 65,72,74,76,82,83,89,91,93,95,98,102,105,108,111,114,115,119,122,128,
%U 132,134,138,139,143,147,151,153,159,161,163,170,175,176,178,182,187
%N Numbers k such that gpf(composite(k)) - lpf(composite(k)) is prime.
%H Robert Israel, <a href="/A154370/b154370.txt">Table of n, a(n) for n = 1..10000</a>
%e Composite(5) = 10 = 5*2 and 5 - 2 = 3 (prime), so 5 is a term;
%e composite(7) = 14 = 7*2 and 7 - 2 = 5 (prime), so 7 is a term;
%e composite(8) = 15 = 5*3 and 5 - 3 = 2 (prime), so 8 is a term;
%e composite(11) = 20 = 5*2*2 and 5 - 2 = 3 (prime), so 11 is a term.
%p A020639 := proc(n) numtheory[factorset](n) ; min(op(%)) ; end proc:
%p A006530 := proc(n) numtheory[factorset](n) ; max(op(%)) ; end proc:
%p for n from 1 to 500 do if isprime( A006530(A002808(n)) - A020639(A002808(n)) ) then printf("%d,",n ) ; end if; end do: # _R. J. Mathar_, May 05 2010
%t Flatten @ Position[Select[Range[1000], CompositeQ], c_Integer /; PrimeQ[Last[#] - First[#]& @ FactorInteger[c][[All, 1]]]] (* _Jean-François Alcover_, Jul 24 2020 *)
%Y Cf. A000040 (primes), A002808 (composites).
%Y Cf. A006530 (gpf), A020639 (lpf).
%K nonn
%O 1,1
%A _Juri-Stepan Gerasimov_, Jan 08 2009
%E Corrected (30 inserted, 43 inserted, 100 removed, ...) by _R. J. Mathar_, May 05 2010
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