cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A209310 Triangular numbers whose sum of triangular divisors is also triangular and greater than 1.

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%I A209310 #16 Aug 12 2023 04:37:38
%S A209310 6,4186,32131,52975,78210,111628,237016,247456,584821,750925,1464616,
%T A209310 3649051,5791906,11297881,16082956,24650731,27243271,38618866,
%U A209310 46585378,51546781,56026405,76923406,89880528,96070591,126906346,164629585,201854278,228733966
%N A209310 Triangular numbers whose sum of triangular divisors is also triangular and greater than 1.
%H A209310 Donovan Johnson, <a href="/A209310/b209310.txt">Table of n, a(n) for n = 1..1000</a>
%e A209310 4186 is in sequence because it is triangular (4186 = 91*92/2) and the sum of its triangular divisors, 4186+91+1 = 4278 is also triangular (4278 = 92*93/2).
%t A209310 triQ[n_] := n > 1 && IntegerQ[Sqrt[8*n+1]]; q[n_] := triQ[1 + DivisorSum[n, #&, triQ[#] &]]; Select[Accumulate[Range[22000]], q] (* _Amiram Eldar_, Aug 12 2023 *)
%o A209310 (PARI) istriangular(n)=issquare(8*n+1)
%o A209310 {t=0; for(n=1, 10^8, if(istriangular(n), k=sumdiv(n, d, istriangular(d)*d) ;if(istriangular(k)&&k>>1,t+=1;write("b209310.txt",t," ",n))))}
%Y A209310 Subsequence of A209309.
%Y A209310 Cf. A000217, A185027, A035316.
%K A209310 nonn
%O A209310 1,1
%A A209310 _Antonio Roldán_, Jan 18 2013