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%I #14 Jun 01 2019 13:22:00
%S 1,12,45,98,116,212,356,531,668,908,909,2036,2192,3425,3548,3771,3871,
%T 4076,4500,4689,4779,5625,5636,6212,6224,8012,8108,8361,8469,8800,
%U 9725,9819,10916,11828,12060,12593,13388,15200,18068,20144,21212,22393,23481,23612
%N Numbers n whose sum of divisors and number of divisors are both triangular numbers.
%H Donovan Johnson, <a href="/A070996/b070996.txt">Table of n, a(n) for n = 1..1000</a>
%t Select[Range[25000],AllTrue[{Sqrt[1+8*DivisorSigma[0,#]],Sqrt[ 1+ 8*DivisorSigma[ 1,#]]},OddQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Jun 01 2019 *)
%o (PARI) c=0; for(n=1, 15891631, s=sigma(n); s2=2*s; r=sqrtint(s2); if(r*(r+1)<>s2, next); nd=numdiv(n); nd2=2*nd; r=sqrtint(nd2); if(r*(r+1)==nd2, c++; write("b070996.txt", c " " n))) /* _Donovan Johnson_, Mar 10 2013 */
%K nonn
%O 1,2
%A _Jason Earls_, May 18 2002
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