

A325560


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


4



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, 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, 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
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OFFSET

1,2


COMMENTS

a(n) is the number of such divisors d of n 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), then that polynomial is a divisor of (0,1)polynomial similarly converted from n, when the polynomial division is done over field GF(2).


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537
Index entries for sequences defined by congruent products between domains N and GF(2)[X]
Index entries for sequences related to polynomials in ring GF(2)[X]


FORMULA

For all n, A325565(n) <= a(n) <= min(A000005(n), A091220(n)).


EXAMPLE

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.


PROG

(PARI) A325560(n) = { my(p = Pol(binary(n))*Mod(1, 2)); sumdiv(n, d, my(q = Pol(binary(d))*Mod(1, 2)); !(p%q)); };


CROSSREFS

Cf. A000005, A048720, A091220, A325559 (positions of 2's), A325563, A325565.
Sequence in context: A035149 A074848 A252505 * A318412 A322986 A167447
Adjacent sequences: A325557 A325558 A325559 * A325561 A325562 A325563


KEYWORD

nonn


AUTHOR

Antti Karttunen, May 11 2019


STATUS

approved



