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%I #12 Jan 16 2020 07:01:49
%S 6,12,18,24,30,36,48,54,60,70,72,90,96,108,120,140,144,150,162,180,
%T 192,198,210,216,240,270,280,286,288,300,324,350,360,384,396,420,432,
%U 450,480,486,490,510,540,560,572,576,594,600,630,646,648,700,720,750,768
%N Numbers k such that the difference of the largest and smallest prime factors of k divides k.
%H Amiram Eldar, <a href="/A083263/b083263.txt">Table of n, a(n) for n = 1..10000</a>
%F Solutions to x mod (A006530(x) - A020639(x)) = 0.
%e Every number k of the form 2^i * 3^j * m is a term because 3 - 2 = 1 is always a divisor of k.
%e Every number k of the form 2 * p * (p+2) * m is a term if p and p+2 form a twin prime pair.
%e Other terms include some in which the difference d = gpf(k) - lpf(k) > 2 is prime (e.g., 30 = 2*3*5 = 3*10; d = 5 - 2 = 3) and some in which it is composite (e.g., 8710 = 2*5*13*67 = 65*134; d = 67 - 2 = 65).
%e All terms are even. - _Jon E. Schoenfield_, Jul 10 2018
%t ffi[x_] := Flatten[FactorInteger[x]]; ba[x_] := Table[Part[ffi[x], 2*w-1], {w, 1, lf[x]}]; lf[x_] := Length[FactorInteger[x]]; ma[x_] := Max[ba[x]]; mi[x_] := Min[ba[x]] Do[s=ma[ba[n]]-mi[ba[n]]; If[Mod[n, s]==0, Print[{n, ba[n], s}]], {n, 1, 10000}]
%Y Cf. A033845, A071141, A006530, A020639.
%K nonn
%O 1,1
%A _Labos Elemer_, May 12 2003
%E Edited by _Jon E. Schoenfield_, Jul 10 2018
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