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A102445 Number of prime divisors (counted with multiplicity) of the central trinomial coefficients (A002426).

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%I A102445 #19 Feb 16 2025 08:32:55
%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,
%T A102445 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,
%U A102445 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
%N A102445 Number of prime divisors (counted with multiplicity) of the central trinomial coefficients (A002426).
%C A102445 First occurrence of k: 1,2,5,11,8,22,17,42,52,26,89,71,80,....
%H A102445 Amiram Eldar, <a href="/A102445/b102445.txt">Table of n, a(n) for n = 1..218</a>
%H A102445 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TrinomialCoefficient.html">Trinomial Coefficient.</a>.
%F A102445 a(n) = A001222(A002426(n)). - _Amiram Eldar_, Feb 06 2020
%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}] (* _Robert G. Wilson v_, Feb 21 2005 *)
%Y A102445 Cf. A001222, A002426.
%K A102445 nonn
%O A102445 1,5
%A A102445 _Jonathan Vos Post_, Feb 21 2005
%E A102445 Edited and extended by _Robert G. Wilson v_, Feb 21 2005