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

1, 3, 10, 63, 147, 156, 225, 234, 408, 600, 680, 684, 952, 1014, 1496, 1500, 1768, 2176, 2584, 3128, 3944, 4216, 4224, 4275, 5032, 5576, 5848, 5880, 6392, 6498, 6660, 6875, 7208, 8024, 8296, 8379, 9112, 9324, 9656, 9840, 9928

Offset: 1

Author

Ctibor O. Zizka, May 30 2009

Keywords

• easy
• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..136 from R. J. Mathar)

Crossrefs

Cf. A000005, A033950.

Programs

Maple

n :=1 :
for k from 1 to 50000 do
    if modp (k,A184389(k)) = 0 then
        printf("%d %d\n",n,k) ;
        n := n+1 ;
    end if;
end do: # R. J. Mathar, Oct 04 2014

Mathematica

t[n_] := n*(n + 1)/2; Select[Range[10^4], Divisible[#, t[DivisorSigma[0, #]]] &] (* Amiram Eldar, Jan 17 2021 *)
dsiQ[n_]:=With[{d=DivisorSigma[0,n]},IntegerQ[n/((d(d+1))/2)]]; Select[Range[10000],dsiQ] (* Harvey P. Dale, Aug 20 2023 *)

PARI

lista(nn) = {for (n=1, nn, if (2*n % (numdiv(n)*(numdiv(n)+1)) == 0, print1(n, ", ")););} \\ Michel Marcus, Jun 02 2013

Extensions

Corrected by Michel Marcus, Jun 02 2013