Search: id:A102445
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%I A102445
%S A102445 0,1,1,1,2,2,2,4,2,2,3,2,2,4,3,4,6,3,2,3,3,5,6,6,4,9,3,3,2,3,3,4,5,3,5,
%T A102445 4,2,3,3,4,2,7,5,7,7,5,5,6,6,4,5,8,9,4,5,6,3,3,7,6,8,7,7,4,5,4,4,7,7,9,
%U A102445 11,5,8,7,7,6,7,7,8,12,4,7,6,6,4,8,7,4,10,7,7,6,6,7,5,5,6,8,7,9,10,5,7
%N A102445 Number of prime divisors (with multiplicity) of the central trinomial 
               coefficients (A002426).
%C A102445 Prime central trinomial coefficients by index: 2,3,4,(2000); semiprimes 
               by index: 5,6,7,9,10,12,13,19,29,37,41,108,(125); 3 prime factors 
               by index: 11,15,18,20,21,27,28,30,31,34,38,39,57,58,105,(125)
%C A102445 First occurrence of k: 1,2,5,11,8,22,17,42,52,26,89,71,80,....
%H A102445 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               TrinomialCoefficient.html">Link to a section of The World of Mathematics.</
               a>.
%t A102445 bigomega[n_Integer] := Plus @@ Last /@ FactorInteger[n]; tn[n_] := Sum[Binomial[n, 
               k]*Binomial[n - k, k], {k, 0, n/2}]; Table[bigomega[tn[n]], {n, 103}] 
               (from Robert G. Wilson v Feb 21 2005)
%Y A102445 Cf. A002426.
%Y A102445 Sequence in context: A102298 A049298 A075016 this_sequence A027389 A160691 
               A049716
%Y A102445 Adjacent sequences: A102442 A102443 A102444 this_sequence A102446 A102447 
               A102448
%K A102445 nonn
%O A102445 1,5
%A A102445 Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 21 2005
%E A102445 Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 21 
               2005

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