A325565 a(n) is the number of such divisors d of n that A048720(A065621(d),n/d) is equal to n.

1, 2, 1, 3, 1, 2, 1, 4, 2, 2, 1, 3, 1, 2, 1, 5, 1, 4, 1, 3, 2, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 6, 2, 2, 2, 6, 1, 2, 1, 4, 1, 4, 1, 3, 2, 2, 1, 5, 2, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 7, 2, 4, 1, 3, 1, 4, 1, 8, 1, 2, 2, 3, 1, 2, 1, 5, 1, 2, 1, 6, 1, 2, 1, 4, 1, 4, 1, 3, 2, 2, 1, 6, 1, 4, 1, 3, 1, 2, 1, 4, 2

Offset

1,2

Comments

Equally, a(n) is number of such pairs of natural numbers t, u that A048720(t,u) = n and A065620(t)*u = n.

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Antti Karttunen, Data supplement: n, a(n) computed 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

a(n) = Sum_{d|n} [A048720(A065621(d),n/d) == n], where [ ] is the Iverson bracket.

a(n) / a(A000265(n)) = A001511(n).

a(n) <= A000005(n) for all n.

a(n) <= A091220(n) for all n.

Prog

(PARI)
A048720(b, c) = fromdigits(Vec(Pol(binary(b))*Pol(binary(c)))%2, 2);
A065621(n) = bitxor(n-1, n+n-1);
A325565(n) = sumdiv(n, d, A048720(A065621(d), n/d)==n);
(PARI)
A065620(n, c=1) = sum(i=0, logint(n+!n, 2), if(bittest(n, i), (-1)^c++<<i)); \\ From A065620
A325565(n) = { my(p = Pol(binary(n))*Mod(1, 2)); sum(d=1, n, my(q = Pol(binary(d))*Mod(1, 2)); (0==(p%q) && (n==(A065620(d)*fromdigits(Vec(lift(p/q)), 2))))); };

Crossrefs

Cf. A000005, A000265, A001511, A048720, A065620, A065621, A091220, A115872, A325566, A325567, A325568, A325569, A325570 (positions of ones).

Sequence in context: A242923 A375040 A065704 * A286552 A324826 A277892

Adjacent sequences: A325562 A325563 A325564 * A325566 A325567 A325568

Keyword

nonn

Author

Antti Karttunen, May 09 2019

Status

approved