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%I #27 Aug 04 2017 03:03:04
%S 2,12,30,56,84,90,132,154,182,220,252,280,306,312,340,374,380,408,418,
%T 420,440,456,462,476,532,552,598,616,624,630,644,650,660,690,756,828,
%U 840,858,870,880,884,900,918,920,936,952,966,986,992,1020,1054,1102
%N Even numbers n such that binomial(n, [n/2]) is divisible by n.
%C 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
%C Conjecture: sequence contains most of 2*A000384(k). Exceptions are k = 8, 18, 20, 23, 35, ... - _Ralf Stephan_, Mar 15 2004
%H David A. Corneth, <a href="/A067348/b067348.txt">Table of n, a(n) for n = 1..12000</a>
%F a(n) = 2*A002503(n-2) + 2.
%F Appears to be 2*A058008(n). - _Benoit Cloitre_, Mar 21 2003
%t Select[Range[2, 1200, 2], Mod[Binomial[ #, #/2], # ]==0&]
%o (PARI) val(n, p) = my(r=0); while(n, r+=n\=p);r
%o 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
%Y Subsequence of A042996.
%Y Cf. A000984, A067315, A080385.
%K nonn
%O 1,1
%A _Dean Hickerson_, Jan 16 2002
%E Name clarified by _Peter Luschny_, Aug 04 2017
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