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.

11, 96, 101, 125, 161, 216, 258, 2754, 5964, 12978, 14496, 31408, 430668, 9660736, 145873104, 181699992, 1140190416, 4573227328, 5927288640

Offset: 1

Author

Paolo P. Lava, Apr 20 2016

Keywords

• nonn
• more
• base

Comments

a(20) > 10^10. - Giovanni Resta, Apr 20 2016

Examples

			sigma(9) * sigma(6) = 13 * 12 = 156 = sigma(96) - 96.
		

Crossrefs

Cf. A253825.

Programs

Maple

with(numtheory); P:=proc(q) local a,b,i,n; for n from 1 to q do
for i from 1 to ilog10(n) do a:=trunc(n/10^i); b:=n-a*10^i;
if sigma(a)*sigma(b)=sigma(n)-n then print(n); break;
fi;  od; od; end: P(10^9);

Mathematica

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 *)
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 *)

Extensions

a(13)-a(19) from Giovanni Resta, Apr 20 2016