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A135189 Numbers n that raised to the powers from 1 to k (with k>=1) are multiple of the sum of their digits (n raised to k+1 must not be a multiple). Case k=4. 13
18, 48, 110, 111, 234, 306, 342, 396, 486, 576, 756, 792, 1010, 1100, 1120, 1164, 1404, 1548, 1566, 1740, 1854, 2106, 2160, 2376, 2430, 2502, 2592, 2640, 2754, 2790, 2850, 2880, 3006, 3060, 3072, 3078, 3180, 3330, 3366, 3420, 3510, 3564, 3690 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..43.

FORMULA

Positive integers n such that A195860(n) = 5.

EXAMPLE

18^1 = 18 -> Sum_digits(18) = 9, and 18 is a multiple of 9.

18^2 = 324 -> Sum_digits(324) = 9, and 324 is a multiple of 9.

18^3 = 5832 -> Sum_digits(5832) = 18, and 5832 is a multiple of 18.

18^4 = 104976 -> Sum_digits(104976) = 27, and 104976 is a multiple of 27

18^5 = 1889568 -> Sum_digits(1889568) = 45, and 1889568 is not a multiple of 45.

MAPLE

readlib(log10); P:=proc(n, m) local a, i, k, w, x, ok; for i from 1 by 1 to n do a:=simplify(log10(i)); if not (trunc(a)=a) then ok:=1; x:=1; while ok=1 do w:=0; k:=i^x; while k>0 do w:=w+k-(trunc(k/10)*10); k:=trunc(k/10); od; if trunc(i^x/w)=i^x/w then x:=x+1; else if x-1=m then print(i); fi; ok:=0; fi; od; fi; od; end: P(2000, 4);

CROSSREFS

Cf. A135186 - A135202.

Sequence in context: A105520 A067726 A234956 * A178398 A222740 A071365

Adjacent sequences:  A135186 A135187 A135188 * A135190 A135191 A135192

KEYWORD

nonn,base

AUTHOR

Paolo P. Lava & Giorgio Balzarotti, Nov 22 2007

EXTENSIONS

More terms from Max Alekseyev, Sep 24 2011

STATUS

approved

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Last modified August 23 06:22 EDT 2017. Contains 290958 sequences.