A135189 Numbers n that raised to the powers from 1 to k (with k>=1) are multiples of the sum of their digits (n raised to k+1 must not be a multiple). Case k=4.

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

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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);

Mathematica

msdQ[n_]:=Module[{t5=n^Range[5]}, AllTrue[#/Total[IntegerDigits[#]]&/@ Most[ t5], IntegerQ]&&!Divisible[Last[t5], Total[IntegerDigits[Last[t5]]]]]; Select[ Range[ 4000], msdQ] (* Harvey P. Dale, Nov 26 2022 *)

Crossrefs

Cf. A135186 - A135202.

Sequence in context: A105520 A067726 A234956 * A178398 A222740 A335377

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