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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. 0
1, 2, 27, 36, 405, 11682, 33651, 669024, 25274655, 40809168, 59716233, 7932651138, 367732181646 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..13.

EXAMPLE

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.

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);

CROSSREFS

Cf. A007953, A124359.

Sequence in context: A041883 A226670 A277542 * A294678 A206585 A046735

Adjacent sequences:  A273841 A273842 A273843 * A273845 A273846 A273847

KEYWORD

nonn,base,more

AUTHOR

Paolo P. Lava, Jun 01 2016

EXTENSIONS

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

STATUS

approved

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Last modified May 6 09:45 EDT 2021. Contains 343580 sequences. (Running on oeis4.)