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%I #17 Apr 06 2023 06:30:18
%S 1,2,4,8,16,32,57,64,65,85,87,128,256,512,1024,1245,1421,2048,3146,
%T 3330,3790,4096,6695,7257,8192,10137,16384,25884,32768,34420,34551,
%U 34947,65536,131072,208495,262144,348161,440495,524288,530270,534430
%N Numbers k such that sigma(k)*k is a triangular number.
%C Infinite, since all the powers of 2 belong to the sequence.
%H Amiram Eldar, <a href="/A115909/b115909.txt">Table of n, a(n) for n = 1..100</a>
%e sigma(1421)*1421 = 2429910 = T(2204).
%t Select[Range[540000],IntegerQ[(Sqrt[1+8(#*DivisorSigma[1,#])]-1)/2]&] (* _Harvey P. Dale_, Dec 16 2011 *)
%o (PARI) isok(n) = ispolygonal(n*sigma(n), 3); \\ _Amiram Eldar_, Apr 06 2023
%Y Cf. A064987, A000217, A115904, A115910.
%K nonn
%O 1,2
%A _Giovanni Resta_, Feb 06 2006