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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.
0
11, 96, 101, 125, 161, 216, 258, 2754, 5964, 12978, 14496, 31408, 430668, 9660736, 145873104, 181699992, 1140190416, 4573227328, 5927288640
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
Cf. A253825.
Sequence in context: A318599 A347479 A051446 * A055286 A081041 A294724
KEYWORD
nonn,more,base
AUTHOR
Paolo P. Lava, Apr 20 2016
EXTENSIONS
a(13)-a(19) from Giovanni Resta, Apr 20 2016
STATUS
approved