A243507 Consider a decimal number, n, with k digits. n = d(k)*10^(k-1) + d(k-1)*10^(k-2) + … + d(2)*10 + d_(1). Sequence lists the numbers n that divide s = Sum_{i=1..k} d(i)^d(i).

1, 2, 3, 4, 5, 6, 7, 8, 9, 63, 64, 93, 377, 643, 699, 760, 2428, 3435, 13073, 46864, 184405, 208858, 1313290, 2326990, 2868720, 2868741, 18273988, 25265859, 33690905, 87889176, 194123725, 589957694

Offset: 1

Author

Paolo P. Lava and Robert G. Wilson v, Jun 05 2014

Keywords

• nonn
• base
• fini

Comments

Since 0^0 is indeterminate, but for all other Xs, X^0 is 1, we define 0^0 here to be 1. (Since 0 does not divide 1, 0 is not a member.)

For Münchhausen numbers (A046253) the ratio is 1. [Paolo P. Lava, Apr 08 2016]

Examples

			63 is in the sequence because 6^6+3^3 = 46683 and 46683/63 = 741, an integer.
		

Crossrefs

Cf. A005188, A046253, A243023.

Programs

Maple

with(numtheory): P:=proc(q) local a,b,k,n; for n from 1 to q do a:=[]; b:=n; while b>0 do a:=[op(a),b mod 10]; b:=trunc(b/10); od; b:=0; for k from 1 to nops(a) do if a[k]=0 then b:=b+1; else b:=b+a[k]^a[k]; fi; od; if type(b/n,integer) then print(n); fi; od; end: P(10^10);

Mathematica

fQ[n_] := Block[{id = IntegerDigits@ n /. {0 -> 1}}, Mod[ Total[ id^id], n] == 0]; k = 1; lst = {}; While[k < 10000000001, If[ fQ@ k, AppendTo[ lst, k]; Print@ k]; k++]; lst