A304107 Analog for squarefree numbers when n is factored in polynomial ring GF(2)[X], so that the binary expansion of n defines the corresponding (0,1)-polynomial. These are numbers n such that the said polynomial doesn't have any duplicated irreducible divisors.

1, 2, 3, 6, 7, 9, 11, 13, 14, 18, 19, 22, 23, 25, 26, 29, 31, 33, 35, 37, 38, 41, 43, 46, 47, 49, 50, 53, 55, 58, 59, 61, 62, 66, 67, 70, 71, 73, 74, 77, 79, 82, 83, 86, 87, 89, 91, 93, 94, 97, 98, 101, 103, 106, 109, 110, 111, 113, 115, 117, 118, 121, 122, 123, 127, 129, 131, 133, 134, 137, 139, 142, 143, 145, 146, 149, 154, 155, 157, 158, 159, 161

Offset

1,2

Comments

Positions of nonzeros in A091219 and A304109. Numbers n such that A091221(n) = A091222(n).

Numbers n that cannot be expressed as n = A048720(k,A000695(m)) for any k >= 0, m >= 2.

It seems that a(n) is approximately 2n for large n. See also comments in A304110.

Links

Antti Karttunen, Table of n, a(n) for n = 1..32769

Index entries for sequences related to polynomials in ring GF(2)[X]

Formula

For n >= 1, A304110(a(n)) = n.

Prog

(PARI)
A304109(n) = { my(fm=factor(Pol(binary(n))*Mod(1, 2))); for(k=1, #fm~, if(fm[k, 2] > 1, return(0))); (1); };
k=0; n=0; while(k<100, n++; if(A304109(n), k++; print1(n, ", ")));

Crossrefs

Cf. A304108 (complement), A304109 (characteristic function), A304110 (least monotonic left inverse).

Cf. A000695, A014580, A048720, A091219, A091221, A091222, A304111.

Cf. also A005117.

Sequence in context: A283208 A259726 A259587 * A344954 A181732 A338901

Adjacent sequences: A304104 A304105 A304106 * A304108 A304109 A304110

Keyword

nonn

Author

Antti Karttunen, May 13 2018

Status

approved