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

1,1

Comments

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

Links

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

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 *)

Prog

(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

Crossrefs

Cf. A000069, A001969, A217790.

Sequence in context: A278855 A137186 A109676 * A211572 A087239 A032653

Adjacent sequences: A223885 A223886 A223887 * A223889 A223890 A223891

Keyword

nonn,base

Author

Vladimir Shevelev, Mar 28 2013

Extensions

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

Status

approved