The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A176996

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A176996

Numbers n such that sum of divisors, sigma(n), and sum of the proper divisors, sigma(n)-n, are both square.
(history; published version)

#27 by Harvey P. Dale at Tue Apr 17 14:48:27 EDT 2018

STATUS

editing

approved

#26 by Harvey P. Dale at Tue Apr 17 14:48:22 EDT 2018

MATHEMATICA

sdQ[n_]:=Module[{d=DivisorSigma[1, n]}, AllTrue[{Sqrt[d], Sqrt[d-n]}, IntegerQ]]; Select[Range[73*10^5], sdQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Apr 17 2018 *)

STATUS

approved

editing

#25 by Michel Marcus at Thu Mar 13 00:55:37 EDT 2014

STATUS

proposed

approved

#24 by Jon E. Schoenfield at Wed Mar 12 23:29:42 EDT 2014

STATUS

editing

proposed

#23 by Jon E. Schoenfield at Wed Mar 12 23:29:39 EDT 2014

PROG

(Sage) is_A176996 = lambda n: is_square(sigma(n)) and is_square(sigma(n)-n) # [_D. S. McNeil, _, Dec 9 09 2010]

CROSSREFS

Cf. A006532, which considers all divisors; A048699, which for non-prime nonprime numbers considers all divisors except the number itself; A073040, which is the union of A048699 and the prime numbers (A000040).

STATUS

approved

editing

#22 by Charles R Greathouse IV at Thu Nov 21 13:12:27 EST 2013

MATHEMATICA

Intersection[Select[Range[10^5], IntegerQ[Sqrt[-# + Plus@@Divisors[#]]] &], Select[Range[10^5], IntegerQ[Sqrt[Plus@@Divisors[#]]] &]] (* From _Alonso del Arte, _, Dec 08 2010 *)

Discussion

Thu Nov 21

13:12

OEIS Server: https://oeis.org/edit/global/2067

#21 by Bruno Berselli at Sun Jul 28 17:59:34 EDT 2013

STATUS

reviewed

approved

#20 by Giovanni Resta at Sun Jul 28 05:24:27 EDT 2013

STATUS

proposed

reviewed

#19 by Jayanta Basu at Sat Jul 27 15:09:28 EDT 2013

STATUS

editing

proposed

#18 by Jayanta Basu at Sat Jul 27 15:09:22 EDT 2013

MATHEMATICA

t = {}; Do[If[And @@ IntegerQ /@ Sqrt[{x = DivisorSigma[1, n], x - n}], AppendTo[t, n]], {n, 10^6}]; t (* Jayanta Basu, Jul 27 2013 *)

STATUS

approved

editing