%I #19 Sep 30 2023 21:44:54
%S 30,70,286,646,1798,3526,7198,10366,20806,23326,38086,44998,64798,
%T 73726,78406,103966,115198,145798,159046,194686,242206,352798,373246,
%U 426886,544966,649798,719998,763846,824326,871198,1312198,1351366,1371166,1472326,1555846
%N Numbers of the form 2*p*q where (p,q) is a twin prime pair.
%C For each term k, A008472(k)/A006530(k) = (2+p+q)/q = (q+q)/q = 2.
%H Donovan Johnson, <a href="/A071142/b071142.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = 2*A037074(n).
%e a(1) = 2 * (product of 1st twin prime pair) = 2*3*5 = 30.
%t ffi[x_] := Flatten[FactorInteger[x]] lf[x_] := Length[FactorInteger[x]] ba[x_] := Table[Part[ffi[x], 2*w-1], {w, 1, lf[x]}] sb[x_] := Apply[Plus, ba[x]] ma[x_] := Part[Reverse[Flatten[FactorInteger[x]]], 2] amo[x_] := Abs[MoebiusMu[x]] Do[s=sb[n]/ma[n]; If[IntegerQ[s]&&Equal[lf[n], 3]&& !Equal[amo[n], 0], Print[{n, ba[n]}]], {n, 2, 1000000}]
%Y Cf. A008472, A006530, A000961, A025475, A037074, A071139-A071147.
%K nonn
%O 1,1
%A _Labos Elemer_, May 13 2002
%E Edited by _Jon E. Schoenfield_, Sep 30 2023