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A325560 a(n) is the number of divisors d of n such that A048720(d,k) = n for some k.

%I A325560 #20 Dec 02 2020 21:33:59
%S A325560 1,2,2,3,2,4,2,4,3,4,2,6,2,4,4,5,2,6,2,6,3,4,2,8,2,4,4,6,2,8,2,6,3,4,
%T A325560 3,9,2,4,3,8,2,6,2,6,6,4,2,10,3,4,4,6,2,8,2,8,3,4,2,12,2,4,6,7,3,6,2,
%U A325560 6,2,6,2,12,2,4,5,6,2,6,2,10,2,4,2,9,4,4,2,8,2,12,2,6,3,4,4,12,2,6,4,6,2,8,2,8,5
%N A325560 a(n) is the number of divisors d of n such that A048720(d,k) = n for some k.
%C A325560 a(n) is the number of divisors d of n such that when the binary expansion of d is converted to a (0,1)-polynomial (e.g., 13=1101[2] encodes X^3 + X^2 + 1), that polynomial is a divisor of the (0,1)-polynomial similarly converted from n, when the polynomial division is done over field GF(2).
%H A325560 Antti Karttunen, <a href="/A325560/b325560.txt">Table of n, a(n) for n = 1..65537</a>
%H A325560 <a href="/index/Con#CongruCrossDomain">Index entries for sequences defined by congruent products between domains N and GF(2)[X]</a>
%H A325560 <a href="/index/Ge#GF2X">Index entries for sequences related to polynomials in ring GF(2)[X]</a>
%F A325560 For all n, A325565(n) <= a(n) <= min(A000005(n), A091220(n)).
%e A325560 39 = 3*13 has four divisors 1, 3, 13, 39, of which all other divisors except 13 are counted because we have A048720(1,39) = A048720(39,1) = A048720(3,29) = 39, but A048720(13,u) is not equal to 39 for any u, thus a(39) = 3. See also the example in A325563.
%o A325560 (PARI) A325560(n) = { my(p = Pol(binary(n))*Mod(1, 2)); sumdiv(n,d,my(q = Pol(binary(d))*Mod(1, 2)); !(p%q)); };
%Y A325560 Cf. A000005, A048720, A091220, A325559 (positions of 2's), A325563, A325565.
%K A325560 nonn
%O A325560 1,2
%A A325560 _Antti Karttunen_, May 11 2019