A070996 Numbers n whose sum of divisors and number of divisors are both triangular numbers.

1, 12, 45, 98, 116, 212, 356, 531, 668, 908, 909, 2036, 2192, 3425, 3548, 3771, 3871, 4076, 4500, 4689, 4779, 5625, 5636, 6212, 6224, 8012, 8108, 8361, 8469, 8800, 9725, 9819, 10916, 11828, 12060, 12593, 13388, 15200, 18068, 20144, 21212, 22393, 23481, 23612

Offset

1,2

Links

Donovan Johnson, Table of n, a(n) for n = 1..1000

Mathematica

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 *)

Prog

(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 */

Crossrefs

Sequence in context: A009785 A135710 A358465 * A350116 A015237 A024223

Adjacent sequences: A070993 A070994 A070995 * A070997 A070998 A070999

Keyword

nonn

Author

Jason Earls, May 18 2002

Status

approved