A166162 Twin prime averages which are also the sum of the divisors of a triangular number.

4, 12, 18, 72, 192, 270, 1488, 1872, 1482, 1872, 1152, 2268, 6552, 3672, 6552, 10890, 3528, 5280, 7560, 7488, 13680, 23040, 17388, 29760, 21600, 23040, 65520, 87120, 51480, 34848, 65268, 127680, 122400, 134400, 114660, 137088, 206640, 134400

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Oct 08 2009

Keywords

• nonn

Examples

			The triangular number A000217(3)= 6 has a sum of divisors 1+2+3+6 = 12 = A014574(3) which is also the average of the twin primes 11 and 13.
		

Crossrefs

Cf. A074285, A014574 [R. J. Mathar, Oct 14 2008]

Programs

Mathematica

t[n_]:=n*(n+1)/2; f[n_]:=Plus@@Divisors[t[n]]; lst={};Do[p=f[n];If[PrimeQ[p-1]&&PrimeQ[p+1], AppendTo[lst,p]],{n,7!}];lst

Extensions

Definition and example rewritten by R. J. Mathar, Oct 14 2009