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A023981 Sum of exponents in prime-power factorization of multinomial coefficient M(5n; n,n,n,n,n).

%I A023981 #11 Jun 11 2025 09:13:34
%S A023981 0,5,10,14,16,22,24,31,29,30,33,40,38,47,49,51,45,53,51,57,59,61,63,
%T A023981 71,66,68,75,73,71,80,78,86,76,80,83,86,81,88,93,97,92,99,100,105,106,
%U A023981 107,108,117,107,112,112,115,118,126,120,124,119,120,127,134,131,139,143,141,127,133
%N A023981 Sum of exponents in prime-power factorization of multinomial coefficient M(5n; n,n,n,n,n).
%H A023981 Amiram Eldar, <a href="/A023981/b023981.txt">Table of n, a(n) for n = 0..10000</a>
%F A023981 From _Amiram Eldar_, Jun 11 2025: (Start)
%F A023981 a(n) = A001222(A008978(n)).
%F A023981 a(n) = A022559(5*n) - 5*A022559(n). (End)
%t A023981 a[n_] := PrimeOmega[Multinomial[n, n, n, n, n]]; Array[a, 100, 0] (* _Amiram Eldar_, Jun 11 2025 *)
%o A023981 (PARI) a(n) = bigomega((5*n)! / n!^5); \\ _Amiram Eldar_, Jun 11 2025
%Y A023981 Cf. A001222, A008978, A022559.
%Y A023981 Cf. A023978, A023979, A023980, A023982, A023983, A023984, A023985, A023986, A023987, A023990, A023991, A023992, A023993.
%K A023981 nonn
%O A023981 0,2
%A A023981 _Clark Kimberling_
%E A023981 Offset changed to 0 and a(0) prepended by _Amiram Eldar_, Jun 11 2025