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A160921 Numbers k such that k / (A000005(k)*(A000005(k)+1)/2) is an integer.

%I A160921 #18 Aug 20 2023 11:44:36
%S A160921 1,3,10,63,147,156,225,234,408,600,680,684,952,1014,1496,1500,1768,
%T A160921 2176,2584,3128,3944,4216,4224,4275,5032,5576,5848,5880,6392,6498,
%U A160921 6660,6875,7208,8024,8296,8379,9112,9324,9656,9840,9928
%N A160921 Numbers k such that k / (A000005(k)*(A000005(k)+1)/2) is an integer.
%H A160921 Amiram Eldar, <a href="/A160921/b160921.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..136 from R. J. Mathar)
%p A160921 n :=1 :
%p A160921 for k from 1 to 50000 do
%p A160921     if modp (k,A184389(k)) = 0 then
%p A160921         printf("%d %d\n",n,k) ;
%p A160921         n := n+1 ;
%p A160921     end if;
%p A160921 end do: # _R. J. Mathar_, Oct 04 2014
%t A160921 t[n_] := n*(n + 1)/2; Select[Range[10^4], Divisible[#, t[DivisorSigma[0, #]]] &] (* _Amiram Eldar_, Jan 17 2021 *)
%t A160921 dsiQ[n_]:=With[{d=DivisorSigma[0,n]},IntegerQ[n/((d(d+1))/2)]]; Select[Range[10000],dsiQ] (* _Harvey P. Dale_, Aug 20 2023 *)
%o A160921 (PARI) lista(nn) = {for (n=1, nn, if (2*n % (numdiv(n)*(numdiv(n)+1)) == 0, print1(n, ", ")););} \\ _Michel Marcus_, Jun 02 2013
%Y A160921 Cf. A000005, A033950.
%K A160921 easy,nonn
%O A160921 1,2
%A A160921 _Ctibor O. Zizka_, May 30 2009
%E A160921 Corrected by _Michel Marcus_, Jun 02 2013