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

1,1

Links

Table of n, a(n) for n=1..38.

Example

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.

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

Crossrefs

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

Sequence in context: A307623 A307624 A177833 * A228166 A244433 A086109

Adjacent sequences: A166159 A166160 A166161 * A166163 A166164 A166165

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Oct 08 2009

Extensions

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

Status

approved