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A325565 a(n) is the number of such divisors d of n that A048720(A065621(d),n/d) is equal to n. 8
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 (list; graph; refs; listen; history; text; internal format)
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: A339914 A242923 A065704 * A286552 A324826 A277892

Adjacent sequences:  A325562 A325563 A325564 * A325566 A325567 A325568

KEYWORD

nonn

AUTHOR

Antti Karttunen, May 09 2019

STATUS

approved

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Last modified July 27 23:16 EDT 2021. Contains 346316 sequences. (Running on oeis4.)