OFFSET
1,2
COMMENTS
Sequence is infinite since it contains all repunits > 0; are there infinitely many other terms?
EXAMPLE
5, 1, 8, 7 are the four digits of 5187. 5^4 = 625 and 6+2+5 = 13; 1^4 = 1; 8^4 = 4096 and 4+0+9+6 = 19; 7^4 = 2401 and 2+4+0+1 = 7. Since 13*1*19*7 = 1729 divides 5187 = 1729*3, 5187 is in the sequence.
MAPLE
P:=proc(n) local i, j, k, w, y, prod, cont; for i from 1 by 1 to n do w:=0; k:=i; cont:=0; while k>0 do k:=trunc(k/10); cont:=cont+1; od; k:=i; prod:=1; for j from 1 to cont do w:=(k-(trunc(k/10)*10))^cont; y:=0; while w>0 do y:=y+w-(trunc(w/10)*10); w:=trunc(w/10); od; prod:=prod*y; k:=trunc(k/10); od; if prod>0 then if trunc(i/prod)=i/prod then print(i); fi; fi; od; end: P(200000);
MATHEMATICA
nddQ[n_]:=Module[{c=Times@@(Total[IntegerDigits[#]]&/@(IntegerDigits[ n]^ IntegerLength[n]))}, c!=0&&Divisible[n, c]]; Select[Range[111111111], nddQ] (* Harvey P. Dale, Jun 05 2016 *)
PROG
(Magma) [ n: n in [1..112000000] | p gt 0 and n mod p eq 0 where p is &*[ &+Intseq(x^#k, 10): x in k ] where k is Intseq(n, 10) ]; // Klaus Brockhaus, Apr 25 2007
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Paolo P. Lava and Giorgio Balzarotti, Apr 18 2007
EXTENSIONS
Edited and a(36) to a(40) added by Klaus Brockhaus, Apr 25 2007
STATUS
approved