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.

A271632 Numbers n = concat(s,t) such that sigma(n) - n = sigma(s) * sigma(t), where sigma(n) - n is the sum of the aliquot parts of n.

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%I A271632 #14 Apr 22 2016 23:46:48
%S A271632 11,96,101,125,161,216,258,2754,5964,12978,14496,31408,430668,9660736,
%T A271632 145873104,181699992,1140190416,4573227328,5927288640
%N A271632 Numbers n = concat(s,t) such that sigma(n) - n = sigma(s) * sigma(t), where sigma(n) - n is the sum of the aliquot parts of n.
%C A271632 a(20) > 10^10. - _Giovanni Resta_, Apr 20 2016
%e A271632 sigma(9) * sigma(6) = 13 * 12 = 156 = sigma(96) - 96.
%p A271632 with(numtheory); P:=proc(q) local a,b,i,n; for n from 1 to q do
%p A271632 for i from 1 to ilog10(n) do a:=trunc(n/10^i); b:=n-a*10^i;
%p A271632 if sigma(a)*sigma(b)=sigma(n)-n then print(n); break;
%p A271632 fi;  od; od; end: P(10^9);
%t A271632 Select[Range[10^5], Function[n, AnyTrue[Function[d, Map[FromDigits, TakeDrop[d, #]] & /@ Range[Length@ d - 1]]@ IntegerDigits@ n, DivisorSigma[1, n] - n == First[DivisorSigma[1, First@ #] DivisorSigma[1, Rest@ #]] &]]] (* _Michael De Vlieger_, Apr 20 2016, Version 10.2 *)
%t A271632 d[n_]:=DivisorSigma[1,n]; ok[n_]:=Block[{p=10, a, r=False, v=d@n-n}, While[(a = Floor[n/p]) > 0 && !r, r = v==d@a d@Mod[n, p]; p*=10]; r]; Select[ Range[10^5], ok] (* _Giovanni Resta_, Apr 20 2016, older Mma *)
%Y A271632 Cf. A253825.
%K A271632 nonn,more,base
%O A271632 1,1
%A A271632 _Paolo P. Lava_, Apr 20 2016
%E A271632 a(13)-a(19) from _Giovanni Resta_, Apr 20 2016