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%I #18 Jan 23 2013 14:39:29
%S 285,1302,1425,1820,2508,3640,3720,4845,4956,5016,5415,7125,7280,9100,
%T 9114,9912,11685,12255,12740,14508,15105,16815,17385,18200,19095,
%U 19824,20235,20805,22134,22515,23655,23660,24021,24738,25365,25480,27075,27588,27645
%N Numbers whose sum of triangular divisors is also a divisor and greater than 1.
%H Antonio Roldán, <a href="/A209311/b209311.txt">Table of n, a(n) for n = 1..13202</a> (terms < 10^7)
%e 285 is in the sequence because its divisors being 1, 3, 5, 15, 19, 57, 95, 285, of which 1, 3 and 15 are triangular, these add up to 19.
%e 1302 is in sequence because the sum of triangular divisors 21 + 6 + 3 + 1 = 31 is divisor of 1302.
%t TriangularQ[n_] := IntegerQ[Sqrt[1 + 8*n]]; fQ[n_] := Module[{tri = Total[Select[Divisors[n], TriangularQ]]}, tri > 1 && Mod[n, tri] == 0]; Select[Range[28000], fQ] (* _T. D. Noe_, Jan 23 2013 *)
%o (PARI) istriangular(n)=issquare(8*n+1)
%o {t=0; for(n=1, 10^7, k=sumdiv(n, d, istriangular(d)*d); if(n/k==n\k&&k>>1, t+=1; write("b209311.txt",t," ",n)))}
%Y Cf. A185027, A035316, A209309, A209310.
%K nonn
%O 1,1
%A _Antonio Roldán_, Jan 18 2013
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