A048197 Numbers k for which binomial(k, floor(k/2)) has more unitary than non-unitary divisors.

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

Author

Labos Elemer

Keywords

• nonn
• more

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

Examples

			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.
		

Crossrefs

Cf. A001405, A034444, A048107, A046098.

Programs

Mathematica

Select[Range[60], Function[n, r = Binomial[n, Floor[n/2]]; 2^(PrimeNu[r] + 1) > DivisorSigma[0, r]]] (* Ivan Neretin, Sep 06 2015 *)

PARI

is(n) = apply(x -> 2^(omega(x)+1) - numdiv(x), binomial(n, n\2)) > 0; \\ Amiram Eldar, Jul 22 2024

Extensions

More terms from Ivan Neretin, Sep 06 2015