|
|
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.
|
|
14
|
|
|
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
|
|
|
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
|
|
|
KEYWORD
|
nonn,base
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|