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

Author

Vladimir Shevelev, Mar 28 2013

Keywords

• nonn
• base

Comments

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

Links

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

Crossrefs

Cf. A000069, A001969, A217790.

Programs

Mathematica

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 *)

PARI

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

Extensions

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