A382239 Numbers not divisible by any of their digits nor by the sum of their digits. Digit 0 is allowed (and does not divide anything).
23, 29, 34, 37, 38, 43, 46, 47, 49, 53, 56, 57, 58, 59, 67, 68, 69, 73, 74, 76, 78, 79, 83, 86, 87, 89, 94, 97, 98, 203, 223, 227, 229, 233, 239, 249, 253, 257, 259, 263, 267, 269, 277, 283, 289, 293, 299, 307, 323, 329, 334, 337, 338, 343, 346, 347, 349, 353, 356, 358, 359, 367, 373, 374, 376
Offset: 1
Examples
a(5) = 38 is included because 38 is not divisible by 3, 8 or 3 + 8 = 11. a(30) = 203 is included because 203 is not divisible by 2, 0, 3 or 2 + 0 + 3 = 5.
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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Maple
filter:= proc(n) local L; L:= subs(0=NULL,convert(n,base,10)); not ormap(t -> n mod t = 0, [op(L),convert(L,`+`)]) end proc: select(filter, [$1..1000]);
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Mathematica
s= {};Do[t=Select[IntegerDigits[n],#>0&];AppendTo[t,Total[t]];If[NoneTrue[t,Mod[n,#]==00&],AppendTo[s,n]],{n,376}];s (* James C. McMahon, Mar 21 2025 *) -
Python
def ok(n): d = list(map(int, str(n))) return (s:=sum(d)) and n%s!=0 and all(n%di!=0 for di in set(d)-{0}) print([k for k in range(1, 377) if ok(k)]) # Michael S. Branicky, Apr 01 2025
Formula
n^k << a(n) < 2^n for n > 5 where k = log(10)/log(9). - Charles R Greathouse IV, Mar 20 2025
Comments