OFFSET
1,1
COMMENTS
a(20) > 10^10. - Giovanni Resta, Apr 20 2016
EXAMPLE
sigma(9) * sigma(6) = 13 * 12 = 156 = sigma(96) - 96.
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 *)
CROSSREFS
KEYWORD
nonn,more,base
AUTHOR
Paolo P. Lava, Apr 20 2016
EXTENSIONS
a(13)-a(19) from Giovanni Resta, Apr 20 2016
STATUS
approved