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URL: https://oeis.org/A048197

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A048197
Numbers k for which binomial(k, floor(k/2)) has more unitary than non-unitary divisors.
0
1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 23, 24, 31, 32, 35, 39, 41, 43, 55, 65, 67, 71, 72, 73, 79, 131, 271, 1567
OFFSET
1,2
COMMENTS
A048107 is applied to central binomial coefficients. This sequence includes the 12 known squarefree central binomial coefficients, i.e., 1, 2, 3, 4, 5, 7, 8, 11, 17, 19, 23, 71 collected in A046098.
Numbers k such that A034444(A001405(k)) > A048105(A001405(k)).
No more terms below 10^5. - Ivan Neretin, Sep 06 2015
EXAMPLE
For k = 59 the corresponding binomial(59,29) has 8192 divisors, of which 4096 are unitary and equally 4096 are non-unitary. So 59 is not in the sequence.
MATHEMATICA
Select[Range[60], Function[n, r = Binomial[n, Floor[n/2]]; 2^(PrimeNu[r] + 1) > DivisorSigma[0, r]]] (* Ivan Neretin, Sep 06 2015 *)
PROG
(PARI) is(n) = apply(x -> 2^(omega(x)+1) - numdiv(x), binomial(n, n\2)) > 0; \\ Amiram Eldar, Jul 22 2024
CROSSREFS
KEYWORD
nonn,more
AUTHOR
EXTENSIONS
More terms from Ivan Neretin, Sep 06 2015
STATUS
approved