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A054905 Smallest composite x such that sigma(x) + 2n = sigma(x + 2n).

%I A054905 #23 Oct 26 2022 23:35:33
%S A054905 434,305635357,104,27,195556,65,12,39,20,56,916,80,212282,57,44,
%T A054905 106645,52,125
%N A054905 Smallest composite x such that sigma(x) + 2n = sigma(x + 2n).
%C A054905 a(19) > 4293000000, if it exists. - _Jud McCranie_, May 25 2000
%C A054905 a(19) > 10^11, if it exists. - _Charles R Greathouse IV_, Oct 26 2022
%H A054905 Mauro Fiorentini, <a href="http://www.bitman.name/math/table/253">Le soluzioni dell’equazione s(n + k) = s(n) + k, con n composto fino a 109 e k sino a 1000</a>.
%e A054905 a(5) corresponds to n=3+2=5, d=2n=10 and the smallest composite integer is 195556. The next solution is 1152136225.
%o A054905 (PARI) a(n)=forcomposite(x=3,10^66,if(sigma(x)+2*n==sigma(x+2*n),return(x)));
%o A054905 for(n=1,66,print1(a(n),", ")); \\ _Joerg Arndt_, Nov 15 2014
%o A054905 (PARI) a19(lim,startAt=39)=startAt=ceil(startAt); my(v=vectorsmall(38),i=(startAt-1)%38); forfactored(n=startAt,lim\1+38, my(t=sigma(n)); if(i++>38,i=1); if(t==v[i]+38, return(n[1]-38)); v[i]=if(vecsum(n[2][,2])>1,t,0)) \\ _Charles R Greathouse IV_, Oct 25 2022
%Y A054905 Cf. A015913, A015914, A015915, A015916, A015917, A054799.
%Y A054905 Cf. A023200, A023201, A023202, A023203,
%K A054905 nonn,more
%O A054905 1,1
%A A054905 _Labos Elemer_ May 23 2000
%E A054905 Description corrected by _Jud McCranie_, May 25 2000