A071142 Numbers of the form 2*p*q where (p,q) is a twin prime pair.

30, 70, 286, 646, 1798, 3526, 7198, 10366, 20806, 23326, 38086, 44998, 64798, 73726, 78406, 103966, 115198, 145798, 159046, 194686, 242206, 352798, 373246, 426886, 544966, 649798, 719998, 763846, 824326, 871198, 1312198, 1351366, 1371166, 1472326, 1555846

Offset: 1

Author

Labos Elemer, May 13 2002

Keywords

• nonn

Comments

For each term k, A008472(k)/A006530(k) = (2+p+q)/q = (q+q)/q = 2.

Examples

			a(1) = 2 * (product of 1st twin prime pair) = 2*3*5 = 30.
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A008472, A006530, A000961, A025475, A037074, A071139-A071147.

Programs

Mathematica

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}]

Formula

a(n) = 2*A037074(n).

Extensions

Edited by Jon E. Schoenfield, Sep 30 2023