cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A154689 #27 Oct 14 2016 08:12:04
%S A154689 5,7,10,13,14,18,19,26,31,38,39,43,50,55,61,62,69,72,73,78,84,86,91,
%T A154689 95,96,98,103,108,109,110,115,119,122,123,129,133,136,138,139,145,146,
%U A154689 151,153,159,181,182,187,190,193,199,205,206,209,213,217,218,219,221,229
%N A154689 Numbers n such that sigma_0(n-sigma_0(n))= sigma_0(n).
%C A154689 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 A154689 Numbers n such that A000005(n-A000005(n)) = A000005(n). - Typo fixed by _Ivan N. Ianakiev_, Oct 08 2016
%H A154689 Harvey P. Dale, <a href="/A154689/b154689.txt">Table of n, a(n) for n = 1..1000</a>
%H A154689 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 A154689 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 A154689 snQ[n_]:=Module[{nd=DivisorSigma[0,n]},DivisorSigma[0,n-nd]==nd]; Select[ Range[300],snQ] (* _Harvey P. Dale_, Nov 10 2011 *)
%o A154689 (PARI) is(n)=my(d=numdiv(n));numdiv(n-d)==d \\ _Charles R Greathouse IV_, Feb 04 2013
%Y A154689 Cf. A000005, A006512 (a subsequence).
%K A154689 easy,nonn
%O A154689 1,1
%A A154689 _Ctibor O. Zizka_, Jan 14 2009
%E A154689 Extended by _R. J. Mathar_, Jan 15 2009