A273844 Least number k such that j*Sd(k) = Sd(k^j) for 1 <= j <= n, where Sd(k) is the sum of the digits of k.

1, 2, 27, 36, 405, 11682, 33651, 669024, 25274655, 40809168, 59716233, 7932651138, 367732181646

Offset: 1

Author

Paolo P. Lava, Jun 01 2016

Keywords

• nonn
• base
• more

Comments

a(14) > 10^12. - Giovanni Resta, Jun 02 2016

Examples

			For n=2, 2*Sd(2) = 2*2 = 4 and Sd(2^2) = Sd(4) = 4.
For n=3, 2*Sd(27) = 2*9 = 18 and Sd(27^2) = Sd(729) = 18;
     and 3*Sd(27) = 3*9 = 27 and Sd(27^3) = Sd(19683) = 27.
		

Crossrefs

Cf. A007953, A124359.

Programs

Maple

T:=proc(w) local x, y, z; x:=w; y:=0; for z from 1 to ilog10(x)+1 do
y:=y+(x mod 10); x:=trunc(x/10); od; y; end:
P:=proc(q) local a,j,k,n,ok,t; t:=1; for k from 1 to q do
for n from t to q do ok:=1; a:=T(n);
for j from 2 to k do if j*a<>T(n^j) then ok:=0; break; fi; od;
if ok=1 then t:=n; print(n); break; fi; od; od; end: P(10^20);

Extensions

a(12)-a(13) from Giovanni Resta, Jun 02 2016