A154689 Numbers n such that sigma_0(n-sigma_0(n))= sigma_0(n).

5, 7, 10, 13, 14, 18, 19, 26, 31, 38, 39, 43, 50, 55, 61, 62, 69, 72, 73, 78, 84, 86, 91, 95, 96, 98, 103, 108, 109, 110, 115, 119, 122, 123, 129, 133, 136, 138, 139, 145, 146, 151, 153, 159, 181, 182, 187, 190, 193, 199, 205, 206, 209, 213, 217, 218, 219, 221, 229

Offset: 1

Author

Ctibor O. Zizka, Jan 14 2009

Keywords

• easy
• nonn

Comments

If n is a term, then n - d(n) is in A175304. Indeed, if N = n - d(n), then d(N) = d(n). Now d(N+d(N)) = d(N+d(n)) = d(n) = d(N). - Vladimir Shevelev, Jul 29 2015

Numbers n such that A000005(n-A000005(n)) = A000005(n). - Typo fixed by Ivan N. Ianakiev, Oct 08 2016

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• J.-M. de Koninck, F. Luca, Positive integers n such that sigma(phi(n))=sigma(n), J. Int. Seq. vol 11 (2008), #08.1.5. [From _R. J. Mathar_, Jan 15 2009]

Crossrefs

Cf. A000005, A006512 (a subsequence).

Programs

Maple

A000005 := proc(n) numtheory[tau](n) ; end: for n from 1 to 1000 do a05 := A000005(n) ; if A000005(n-a05) = a05 then printf("%d,",n) ; fi; od: # R. J. Mathar, Jan 15 2009

Mathematica

snQ[n_]:=Module[{nd=DivisorSigma[0,n]},DivisorSigma[0,n-nd]==nd]; Select[ Range[300],snQ] (* Harvey P. Dale, Nov 10 2011 *)

PARI

is(n)=my(d=numdiv(n));numdiv(n-d)==d \\ Charles R Greathouse IV, Feb 04 2013

Extensions

Extended by R. J. Mathar, Jan 15 2009