A067348 Even numbers n such that binomial(n, [n/2]) is divisible by n.

2, 12, 30, 56, 84, 90, 132, 154, 182, 220, 252, 280, 306, 312, 340, 374, 380, 408, 418, 420, 440, 456, 462, 476, 532, 552, 598, 616, 624, 630, 644, 650, 660, 690, 756, 828, 840, 858, 870, 880, 884, 900, 918, 920, 936, 952, 966, 986, 992, 1020, 1054, 1102

Offset

1,1

Comments

This sequence has a surprisingly large overlap with A080385(n); a few values, 2, 420, 920 are exceptional. This means that usually A080383(A067348(n))=7. - Labos Elemer, Mar 17 2003

Conjecture: sequence contains most of 2*A000384(k). Exceptions are k = 8, 18, 20, 23, 35, ... - Ralf Stephan, Mar 15 2004

Links

David A. Corneth, Table of n, a(n) for n = 1..12000

Formula

a(n) = 2*A002503(n-2) + 2.

Appears to be 2*A058008(n). - Benoit Cloitre, Mar 21 2003

Mathematica

Select[Range[2, 1200, 2], Mod[Binomial[ #, #/2], # ]==0&]

Prog

(PARI) val(n, p) = my(r=0); while(n, r+=n\=p); r
is(n) = {if(valuation(n, 2) == 0, return(0)); my(f = factor(n)); for(i=1, #f~, if(val(n, f[i, 1]) - 2 * val(n/2, f[i, 1]) - f[i, 2] < 0, return(0))); return(1)} \\ David A. Corneth, Jul 29 2017

Crossrefs

Subsequence of A042996.

Cf. A000984, A067315, A080385.

Sequence in context: A061780 A249411 A156021 * A002939 A118239 A249055

Adjacent sequences: A067345 A067346 A067347 * A067349 A067350 A067351

Keyword

nonn

Author

Dean Hickerson, Jan 16 2002

Extensions

Name clarified by Peter Luschny, Aug 04 2017

Status

approved