A048197 - OEIS

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

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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

LINKS

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

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

Cf. A001405, A034444, A048107, A046098.

Sequence in context: A105208 A074779 A253567 * A253784 A342191 A251726

Adjacent sequences: A048194 A048195 A048196 * A048198 A048199 A048200

KEYWORD

nonn,more

AUTHOR

Labos Elemer

EXTENSIONS

More terms from Ivan Neretin, Sep 06 2015

STATUS

approved