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A325565
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a(n) is the number of such divisors d of n that A048720(A065621(d),n/d) is equal to n.
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8
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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
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OFFSET
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1,2
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COMMENTS
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Equally, a(n) is number of such pairs of natural numbers t, u that A048720(t,u) = n and A065620(t)*u = n.
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LINKS
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FORMULA
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a(n) = Sum_{d|n} [A048720(A065621(d),n/d) == n], where [ ] is the Iverson bracket.
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PROG
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(PARI)
A048720(b, c) = fromdigits(Vec(Pol(binary(b))*Pol(binary(c)))%2, 2);
(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))))); };
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CROSSREFS
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Cf. A000005, A000265, A001511, A048720, A065620, A065621, A091220, A115872, A325566, A325567, A325568, A325569, A325570 (positions of ones).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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