A384427 Evil numbers that are not a multiple of any other evil number.

3, 5, 17, 23, 29, 43, 53, 71, 77, 83, 89, 101, 113, 139, 149, 163, 169, 197, 209, 257, 263, 269, 277, 281, 287, 293, 311, 317, 329, 337, 343, 347, 349, 353, 359, 373, 383, 389, 401, 407, 413, 427, 449, 461, 467, 469, 479, 503, 509, 523, 533, 547, 553, 571, 593, 599

Offset: 1

Author

Francisco J. Muñoz, May 28 2025

Keywords

• nonn
• base

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Union of A217790 and A027699.

Cf. A001969, A129771.

Programs

Maple

isevil:= proc(n) convert(convert(n,base,2),`+`)::even end proc:
N:= 1000: # for terms <= N
V:= Vector(N,1):
for i from 1 to N do
    if isevil(i) then V[[seq(j,j=2*i .. N, i)]]:= 0
    else V[i]:= 0
    fi
od:
select(t -> V[t]=1, [$1..N]); # Robert Israel, Jun 18 2025

Mathematica

evilQ[n_] := EvenQ[DigitCount[n, 2, 1]]; q[n_] := evilQ[n] && AllTrue[Divisors[n], # == n || ! evilQ[#] &]; Select[Range[600], q] (* Amiram Eldar, May 31 2025 *)

PARI

isevil(n) = hammingweight(n) % 2 == 0;
noevildiv(n) = {fordiv(n, d, if ((d < n) && isevil(d), return (0)); ); 1; }
isok(n) = isevil(n) && noevildiv(n); \\ Michel Marcus, May 31 2025