A048197 Numbers n for which binomial(n, floor(n/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

1,2

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.

No more terms below 10^5. - Ivan Neretin, Sep 06 2015

Links

Table of n, a(n) for n=1..37.

Formula

A034444(A001405(n)) > A048105(A001405(n)).

Example

n=59 when the corresponding binomial(59,29) has 8192 divisors, of which 4096 are unitary and equally 4096 are not such ones. 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 *)

Crossrefs

Cf. A001405, A034444, A048107, A046098.

Sequence in context: A105208 A074779 A253567 * A253784 A342191 A251726

Adjacent sequences: A048194 A048195 A048196 * A048198 A048199 A048200

Keyword

nonn

Author

Labos Elemer

Extensions

More terms from Ivan Neretin, Sep 06 2015

Status

approved