A115907 Numbers k such that sigma(k) plus the k-th prime is a triangular number.

1, 2, 9, 13, 21, 80, 112, 129, 147, 225, 308, 349, 1063, 1282, 1300, 1635, 1880, 2686, 2956, 3517, 3759, 3907, 4058, 5025, 5196, 6742, 7606, 7708, 9244, 10154, 10596, 11259, 11719, 12687, 13167, 13599, 14081, 14624, 15937, 16437, 16766, 18289

Offset

1,2

Links

David A. Corneth, Table of n, a(n) for n = 1..11241 (first 1000 from Robert Israel)

Example

sigma(1880) + prime(1880) = 20503 = T(202).

Maple

filter:= n -> issqr(1+8*(numtheory:-sigma(n)+ithprime(n))):
select(filter, [$1..10^5]); # Robert Israel, Nov 07 2018

Mathematica

Select[Range[25000], IntegerQ[(Sqrt[8(DivisorSigma[1, #]+Prime[#])+ 1]-1)/2]&] (* Harvey P. Dale, Jun 07 2011 *)

Prog

(PARI) upto(n) = my(t = 0, res = List(), u = prime(n)); forprime(p = 2, u, t++; c = p + sigma(t); if(ispolygonal(c, 3), listput(res, t))); res \\ David A. Corneth, Nov 08 2018

Crossrefs

Cf. A000040, A000203, A000217, A115882, A115908.

Sequence in context: A234902 A138946 A037385 * A063634 A178688 A163735

Adjacent sequences: A115904 A115905 A115906 * A115908 A115909 A115910

Keyword

nonn

Author

Giovanni Resta, Feb 06 2006

Status

approved