

A102445


Number of prime divisors (with multiplicity) of the central trinomial coefficients (A002426).


2



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, 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, 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
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OFFSET

1,5


COMMENTS

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)
First occurrence of k: 1,2,5,11,8,22,17,42,52,26,89,71,80,....


LINKS

Table of n, a(n) for n=1..103.
Eric Weisstein's World of Mathematics, Trinomial Coefficient..


MATHEMATICA

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}] (* Robert G. Wilson v, Feb 21 2005 *)


CROSSREFS

Cf. A002426.
Sequence in context: A049298 A075016 A279409 * A160691 A049716 A188903
Adjacent sequences: A102442 A102443 A102444 * A102446 A102447 A102448


KEYWORD

nonn


AUTHOR

Jonathan Vos Post, Feb 21 2005


EXTENSIONS

Edited and extended by Robert G. Wilson v, Feb 21 2005


STATUS

approved



