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A379120 a(1) = 1; and for n > 1, a(n) is the smallest divisor d > 1 of n such that A048720(A065621(n/d),d) is equal to n.

%I A379120 #10 Dec 17 2024 21:23:50
%S A379120 1,2,3,2,5,3,7,2,3,5,11,3,13,7,15,2,17,3,19,5,7,11,23,3,25,13,27,7,29,
%T A379120 15,31,2,3,17,7,3,37,19,39,5,41,7,43,11,15,23,47,3,7,25,51,13,53,27,
%U A379120 55,7,57,29,59,15,61,31,63,2,5,3,67,17,69,7,71,3,73,37,15,19,77,39,79,5,81,41,83,7,85,43,87,11,89
%N A379120 a(1) = 1; and for n > 1, a(n) is the smallest divisor d > 1 of n such that A048720(A065621(n/d),d) is equal to n.
%H A379120 Antti Karttunen, <a href="/A379120/b379120.txt">Table of n, a(n) for n = 1..65537</a>
%H A379120 <a href="/index/Con#CongruCrossDomain">Index entries for sequences defined by congruent products between domains N and GF(2)[X]</a>.
%H A379120 <a href="/index/Ge#GF2X">Index entries for sequences related to polynomials in ring GF(2)[X]</a>.
%F A379120 a(n) = n / A325567(n).
%o A379120 (PARI)
%o A379120 A048720(b,c) = fromdigits(Vec(Pol(binary(b))*Pol(binary(c)))%2, 2);
%o A379120 A065621(n) = bitxor(n-1,n+n-1);
%o A379120 A379120(n) = if(1==n,n,fordiv(n,d,if((d>1)&&A048720(A065621(n/d),d)==n,return(d))));
%Y A379120 Cf. A048720, A065621, A115872, A325565, A325566, A325567.
%Y A379120 Cf. also A379119.
%K A379120 nonn
%O A379120 1,2
%A A379120 _Antti Karttunen_, Dec 17 2024