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%I #21 Nov 09 2018 22:10:43
%S 1,2,9,13,21,80,112,129,147,225,308,349,1063,1282,1300,1635,1880,2686,
%T 2956,3517,3759,3907,4058,5025,5196,6742,7606,7708,9244,10154,10596,
%U 11259,11719,12687,13167,13599,14081,14624,15937,16437,16766,18289
%N Numbers k such that sigma(k) plus the k-th prime is a triangular number.
%H David A. Corneth, <a href="/A115907/b115907.txt">Table of n, a(n) for n = 1..11241</a> (first 1000 from Robert Israel)
%e sigma(1880) + prime(1880) = 20503 = T(202).
%p filter:= n -> issqr(1+8*(numtheory:-sigma(n)+ithprime(n))):
%p select(filter, [$1..10^5]); # _Robert Israel_, Nov 07 2018
%t Select[Range[25000],IntegerQ[(Sqrt[8(DivisorSigma[1,#]+Prime[#])+ 1]-1)/2]&] (* _Harvey P. Dale_, Jun 07 2011 *)
%o (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
%Y Cf. A000040, A000203, A000217, A115882, A115908.
%K nonn
%O 1,2
%A _Giovanni Resta_, Feb 06 2006