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A048196
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Numbers k for which binomial(k, floor(k/2)) has the same number of unitary and non-unitary divisors.
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1
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14, 22, 33, 42, 44, 56, 57, 59, 74, 107, 113, 115, 1568, 1571
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OFFSET
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1,1
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COMMENTS
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Numbers k where b = binomial(k, floor(k/2)) is of the form p_i ^ e_i where p_i is the i-th prime in the factorization of b, e_i = 1 except exactly one e_i = 3 for i > 1. - David A. Corneth, May 13 2018
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LINKS
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FORMULA
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EXAMPLE
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At k=59, the corresponding binomial coefficient, binomial(59,29) has 8192 divisors, of which 4096 are unitary and 4096 are not.
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PROG
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(PARI) isok(n) ={ n=binomial(n, floor(n/2)); sumdiv(n, d, issquarefree(d)) == sumdiv(n, d, !issquarefree(d)); } \\ Joerg Arndt, May 13 2018
(PARI) \\ much faster:
isok(n) ={ n=binomial(n, floor(n/2)); my(u=1<<omega(n)); u==numdiv(n)-u; } \\ Joerg Arndt, May 13 2018
(PARI) \\ for a still faster program see the Corneth link.
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CROSSREFS
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KEYWORD
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nonn,hard
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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