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%I #15 Dec 25 2016 02:35:09
%S 1,2,3,4,5,6,7,11,13,14,16,17,18,19,23,24,25,28,29,31,33,36,37,41,43,
%T 47,51,53,54,59,61,66,67,71,73,79,83,89,91,97,101,103,107,109,112,113,
%U 123,127,131,135,137,139,149,151,157,163,167,172,173,179,181,191,193
%N Numbers n such that sum of proper divisors s(n) is a triangular number T(k).
%H Robert Israel, <a href="/A045745/b045745.txt">Table of n, a(n) for n = 1..10000</a>
%e s(14)=1+2+7=10 is a triangular number. In fact T(4)=10.
%p select(t -> issqr(1+8*(numtheory:-sigma(t)-t)), [$1..1000]); # _Robert Israel_, Dec 25 2016
%t tri[ n_ ] := Module[ {}, a=Floor[ N[ Sqrt[ 2n ] ] ]; a(a+1)/2==n ]; Select[ Range[ 300 ], tri[ Apply[ Plus, Divisors[ # ] ]-# ]& ]
%Y Cf. A000217.
%K nonn,easy
%O 1,2
%A _Felice Russo_
%E More terms from _Erich Friedman_
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