cp's OEIS Frontend

A023978 Sum of exponents in prime-power factorization of multinomial coefficient M(3n; n,n,n).

%I A023978 #13 Jun 11 2025 09:13:11
%S A023978 0,2,4,7,7,9,11,14,12,13,14,19,18,20,22,23,19,23,22,27,25,25,30,33,30,
%T A023978 30,32,33,31,34,34,38,33,34,36,38,34,37,40,42,39,42,43,50,49,48,50,54,
%U A023978 49,50,49,51,51,53,54,55,51,53,54,61,57,60,63,63,56,56,56,61,60,61,63,66,61,64,67,69,67,68
%N A023978 Sum of exponents in prime-power factorization of multinomial coefficient M(3n; n,n,n).
%H A023978 Amiram Eldar, <a href="/A023978/b023978.txt">Table of n, a(n) for n = 0..10000</a>
%F A023978 From _Amiram Eldar_, Jun 11 2025: (Start)
%F A023978 a(n) = A001222(A006480(n)).
%F A023978 a(n) = A022559(3*n) - 3*A022559(n). (End)
%t A023978 a[n_] := PrimeOmega[Multinomial[n, n, n]]; Array[a, 100, 0] (* _Amiram Eldar_, Jun 11 2025 *)
%o A023978 (PARI) a(n) = bigomega((3*n)! / n!^3); \\ _Amiram Eldar_, Jun 11 2025
%Y A023978 Cf. A001222, A006480, A022559.
%Y A023978 Cf. A023979, A023980, A023981, A023982, A023983, A023984, A023985, A023986, A023987, A023990, A023991, A023992, A023993.
%K A023978 nonn
%O A023978 0,2
%A A023978 _Clark Kimberling_
%E A023978 Offset changed to 0 and a(0) prepended by _Amiram Eldar_, Jun 11 2025