A217790 -id:A217790 - cp's OEIS frontend

A223888 Composite odious numbers (A000069) having no proper odious divisors greater than 1.

25, 69, 81, 87, 115, 145, 213, 265, 289, 339, 355, 391, 415, 445, 477, 493, 505, 529, 565, 695, 731, 747, 789, 815, 841, 901, 985, 1041, 1047, 1077, 1119, 1149, 1207, 1219, 1315, 1341, 1347, 1383, 1401, 1411, 1437, 1465, 1509, 1513, 1527, 1537, 1555, 1585

Offset: 1

Vladimir Shevelev, Mar 28 2013

The sequence is obtained using Eratosthenes-like sieve for odious numbers.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A000069, A001969, A217790.

odiousQ[n_] := OddQ@Total@IntegerDigits[n, 2]; okQ[n_] := n > 1 && odiousQ[n] && ! PrimeQ[n] && Catch[Do[If[odiousQ[d], Throw[False]], {d, Most@Rest@Divisors@n}]; True]; Select[Range@3000, okQ] (* Giovanni Resta, Mar 28 2013 *)

isodi(n) = hammingweight(n) % 2;
noodid(n) = {fordiv(n, d, if ((d != 1) && (d < n) && isodi(d), return (0));); 1;}
lista(nn) = {forcomposite(n=1, nn, if (isodi(n) && noodid(n), print1(n, ", ")););} \\ Michel Marcus, Feb 08 2016

a(10)-a(48) from Giovanni Resta, Mar 28 2013

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

Original entry on oeis.org

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

Francisco J. Muñoz, May 28 2025

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

Union of A217790 and A027699.

Cf. A001969, A129771.

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

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 *)

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

cp's OEIS Frontend

A223888 Composite odious numbers (A000069) having no proper odious divisors greater than 1.

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