cp's OEIS Frontend

A329704 Numbers k such that the sum of divisors of k (A000203) and the sum of proper divisors of k (A001065) are both triangular numbers (A000217).

%I A329704 #18 Mar 03 2020 08:50:44
%S A329704 1,2,5,36,54,441,473,6525,52577,124025,683820,1513754,1920552,6079931,
%T A329704 6762923,14751657,17052782,17310942,36543714,49919939,60260967,
%U A329704 251849052,364535720,372476909,562047389,670395564,670440852,783856979,824626800,1084201689,1122603809
%N A329704 Numbers k such that the sum of divisors of k (A000203) and the sum of proper divisors of k (A001065) are both triangular numbers (A000217).
%C A329704 Are 1 and 36 the only terms that are also triangular numbers?
%C A329704 No other triangular terms up to A000217(10^8). - _Michel Marcus_, Mar 01 2020
%H A329704 Amiram Eldar, <a href="/A329704/b329704.txt">Table of n, a(n) for n = 1..48</a>
%e A329704 5 is a term since sigma(5) = 6 and sigma(5) - 5 = 1 are both triangular numbers.
%t A329704 triQ[n_] := IntegerQ @ Sqrt[8*n+1]; Select[Range[10^5], triQ[(s = DivisorSigma[1, #])] && triQ[s - #] &]
%o A329704 (PARI) isok(k) = my(s=sigma(k)); ispolygonal(s, 3) && ispolygonal(s-k, 3); \\ _Michel Marcus_, Feb 29 2020
%Y A329704 Intersection of A045745 and A045746.
%Y A329704 Cf. A000203, A000217, A001065.
%K A329704 nonn
%O A329704 1,2
%A A329704 _Amiram Eldar_, Feb 28 2020