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

1,1

Comments

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

Links

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

Formula

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

Example

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

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}]

Crossrefs

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

Sequence in context: A357854 A071141 A071312 * A218327 A259753 A308137

Adjacent sequences: A071139 A071140 A071141 * A071143 A071144 A071145

Keyword

nonn

Author

Labos Elemer, May 13 2002

Extensions

Edited by Jon E. Schoenfield, Sep 30 2023

Status

approved