

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.


5



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
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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 * A181732 A190199 A014873
Adjacent sequences: A304104 A304105 A304106 * A304108 A304109 A304110


KEYWORD

nonn


AUTHOR

Antti Karttunen, May 13 2018


STATUS

approved



