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Numbers n such that sigma_0(n-sigma_0(n))= sigma_0(n).
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%I #27 Oct 14 2016 08:12:04

%S 5,7,10,13,14,18,19,26,31,38,39,43,50,55,61,62,69,72,73,78,84,86,91,

%T 95,96,98,103,108,109,110,115,119,122,123,129,133,136,138,139,145,146,

%U 151,153,159,181,182,187,190,193,199,205,206,209,213,217,218,219,221,229

%N Numbers n such that sigma_0(n-sigma_0(n))= sigma_0(n).

%C 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

%C Numbers n such that A000005(n-A000005(n)) = A000005(n). - Typo fixed by _Ivan N. Ianakiev_, Oct 08 2016

%H Harvey P. Dale, <a href="/A154689/b154689.txt">Table of n, a(n) for n = 1..1000</a>

%H J.-M. de Koninck, F. Luca, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL11/DeKoninck/dekoninck47.html">Positive integers n such that sigma(phi(n))=sigma(n)</a>, J. Int. Seq. vol 11 (2008), #08.1.5. [From _R. J. Mathar_, Jan 15 2009]

%p 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

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

%o (PARI) is(n)=my(d=numdiv(n));numdiv(n-d)==d \\ _Charles R Greathouse IV_, Feb 04 2013

%Y Cf. A000005, A006512 (a subsequence).

%K easy,nonn

%O 1,1

%A _Ctibor O. Zizka_, Jan 14 2009

%E Extended by _R. J. Mathar_, Jan 15 2009