%I #14 Feb 01 2023 04:57:33
%S 10,14,15,20,26,28,30,35,38,40,42,45,50,52,56,60,62,70,75,76,78,80,84,
%T 86,90,98,100,104,112,114,120,122,124,126,130,135,140,143,146,150,152,
%U 156,160,168,172,175,180,182,186,190,196,200,206,208,210,218,224,225
%N Numbers n such that the difference between the largest distinct prime divisor and the smallest distinct prime divisor is a prime.
%C Obviously all terms are composite, because for primes the difference is zero. - _R. J. Mathar_, Feb 01 2023
%H Harvey P. Dale, <a href="/A119613/b119613.txt">Table of n, a(n) for n = 1..1000</a>
%e If n = 10 then the prime divisors are 2 and 5 and the difference between these two is 3 which is also a prime. So 10 is in the sequence.
%e If n = 70 then the prime divisors are 2, 5 and 7 and the difference between the largest and the smallest distinct prime divisors is 5 which is also a prime. So 70 is in the sequence.
%t Select[Range[2,300],Not[Length[FactorInteger[ # ]]==1]&&PrimeQ[FactorInteger[ # ][[ -1, 1]] -FactorInteger[ # ][[1, 1]]] &] (* _Stefan Steinerberger_, Jun 06 2006 *)
%t pQ[n_]:=Module[{fi=FactorInteger[n]},Length[fi]>1&&PrimeQ[fi[[-1,1]]-fi[[1,1]]]]; Select[Range[250],pQ] (* _Harvey P. Dale_, Nov 19 2019 *)
%K nonn,less
%O 1,1
%A _Parthasarathy Nambi_, Jun 05 2006
%E Corrected and extended by _Stefan Steinerberger_, Jun 06 2006