A048197 - OEIS

%I #21 Jul 22 2024 15:22:27

%S 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,

%T 43,55,65,67,71,72,73,79,131,271,1567

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

%C 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.

%C Numbers k such that A034444(A001405(k)) > A048105(A001405(k)).

%C No more terms below 10^5. - _Ivan Neretin_, Sep 06 2015

%e 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.

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

%o (PARI) is(n) = apply(x -> 2^(omega(x)+1) - numdiv(x), binomial(n, n\2)) > 0; \\ _Amiram Eldar_, Jul 22 2024

%Y Cf. A001405, A034444, A048107, A046098.

%K nonn,more

%O 1,2

%A _Labos Elemer_

%E More terms from _Ivan Neretin_, Sep 06 2015