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A019469
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Numbers k such that k does not divide binomial(2*k-4, k-2).
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4
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2, 3, 4, 6, 8, 9, 12, 15, 16, 27, 30, 32, 33, 36, 39, 42, 64, 81, 84, 87, 90, 93, 96, 108, 111, 114, 117, 120, 123, 128, 243, 246, 249, 252, 255, 256, 258, 270, 273, 276, 279, 282, 285, 324, 327, 330, 333, 336, 339
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OFFSET
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1,1
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COMMENTS
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Previous name was: Numbers n such that (n-2)-nd Catalan number is not divisible by n.
Conjecture (confirmed, see links): sequence is union of powers of two > 1 (A000079) and 3 * A096304.
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LINKS
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MAPLE
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MATHEMATICA
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Select[Range[400], !Divisible[Binomial[2#-4, #-2], #]&] (* Harvey P. Dale, Aug 13 2015 *)
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PROG
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(PARI) valp(n, p)=my(s); while(n\=p, s+=n); s
bin(n, p)=valp(2*n, p)-2*valp(n, p)
is(n)=my(f=factor(n)); for(i=1, #f~, if(bin(n-2, f[i, 1])<f[i, 2], return(1))); 0 \\ Charles R Greathouse IV, Nov 04 2016
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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