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.

A076495 Smallest x such that sigma(x) mod x = n, or 0 if no such x exists.

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%I A076495 #34 Jun 03 2019 02:09:35
%S A076495 2,20,4,9,0,25,8,10,15,14,21,24,27,22,16,26,39,208,36,34,51,38,57,112,
%T A076495 95,46,69,48,115,841,32,58,45,62,93,660,155,1369,162,44,63,1681,50,82,
%U A076495 123,52,129,60,75,94,72,352,235,90,329,84,99,68,265,96,371,118,64,76
%N A076495 Smallest x such that sigma(x) mod x = n, or 0 if no such x exists.
%C A076495 At present, the 0 entry for n=5 is only a conjecture.
%C A076495 For n <= 1000, a(5) and a(898) are the only terms not found using x <= 10^11. - _Donovan Johnson_, Sep 20 2012
%C A076495 10^11 < a(898) <= 140729946996736. - _Donovan Johnson_, Sep 28 2013
%C A076495 a(898) > 10^13 and the same bound holds for a(5), if it exists. - _Giovanni Resta_, Apr 02 2014
%C A076495 a(5) > 1.5*10^14, if it exists. - _Jud McCranie_, Jun 02 2019
%H A076495 Donovan Johnson, <a href="/A076495/b076495.txt">Table of n, a(n) for n = 1..1000</a>
%H A076495 Carl Pomerance, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa26/aa2637.pdf">On the congruences σ(n) ≡ a (mod n) and n ≡ a (mod φ(n))</a>, Acta Arithmetica 26:3 (1974-1975), pp. 265-272. (See theorem 4.)
%e A076495 n=1: a(1) = smallest prime = 2.
%e A076495 n=3: a(3) = 4 since sigma(4) mod 4 = 7 mod 4 = 3.
%e A076495 n=5: Very difficult case (see Comments section).
%t A076495 f[x_] := s=Mod[DivisorSigma[1, n], n]; t=Table[0, {256}]; Do[s=f[n]; If[s<257&&t[[s]]==0, t[[s]]=n], {n, 1, 10000000}]; t
%o A076495 (PARI) a(n)=my(k);while(sigma(k++)%k!=n,);k \\ _Charles R Greathouse IV_, Dec 28 2013
%Y A076495 Cf. A045768, A045769, A045770, A054024.
%K A076495 nonn
%O A076495 1,1
%A A076495 _Labos Elemer_, Oct 21 2002