login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

%I #21 Jul 02 2018 07:02:40

%S 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,

%T 49,50,53,55,58,59,61,62,66,67,70,71,73,74,77,79,82,83,86,87,89,91,93,

%U 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

%N 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.

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

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

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

%H Antti Karttunen, <a href="/A304107/b304107.txt">Table of n, a(n) for n = 1..32769</a>

%H <a href="/index/Ge#GF2X">Index entries for sequences related to polynomials in ring GF(2)[X]</a>

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

%o (PARI)

%o A304109(n) = { my(fm=factor(Pol(binary(n))*Mod(1, 2))); for(k=1, #fm~, if(fm[k, 2] > 1, return(0))); (1); };

%o k=0; n=0; while(k<100, n++; if(A304109(n), k++; print1(n,", ")));

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

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

%Y Cf. also A005117.

%K nonn

%O 1,2

%A _Antti Karttunen_, May 13 2018

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 06:57 EDT 2024. Contains 371265 sequences. (Running on oeis4.)