

A067348


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


9



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
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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(n2) + 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



