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A081392 Numbers k such that the central binomial coefficient C(k, floor(k/2)) has only one prime divisor whose exponent is greater than one. 0
6, 9, 12, 13, 14, 15, 16, 18, 20, 21, 22, 24, 31, 32, 33, 35, 39, 41, 42, 43, 44, 55, 56, 57, 58, 59, 60, 61, 62, 65, 67, 72, 73, 74, 79, 107, 108, 109, 110, 113, 114, 115, 116, 131, 159, 219, 220, 271, 319, 341, 342, 1567, 1568, 1571, 1572 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

As expected, the (single) non-unitary prime divisors for C(2k, k) and C(k, floor(k/2)) or for Catalan numbers equally come from the smallest prime(s).

Numbers k such that A001405(k) is in A190641. - Michel Marcus, Jul 30 2017

LINKS

Table of n, a(n) for n=1..55.

EXAMPLE

For k=341, binomial(341,170) = 2*2*2*2*M, where M is a squarefree product of 48 further prime factors.

MATHEMATICA

pde1Q[n_]:=Length[Select[FactorInteger[Binomial[n, Floor[n/2]]], #[[2]]> 1&]] == 1; Select[Range[1600], pde1Q] (* Harvey P. Dale, Jan 21 2019 *)

PROG

(PARI) isok(n) = my(f=factor(binomial(n, n\2))); #select(x->(x>1), f[, 2]) == 1; \\ Michel Marcus, Jul 30 2017

CROSSREFS

Cf. A000108, A000984, A001405, A046098, A080664, A081386-A081391, A190641.

Sequence in context: A143710 A087022 A315951 * A225868 A185177 A185179

Adjacent sequences:  A081389 A081390 A081391 * A081393 A081394 A081395

KEYWORD

nonn,more

AUTHOR

Labos Elemer, Mar 27 2003

EXTENSIONS

a(52)-a(55) from Michel Marcus, Jul 30 2017

STATUS

approved

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Last modified May 21 03:05 EDT 2019. Contains 323434 sequences. (Running on oeis4.)