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A023987 Sum of exponents of primes in C(5n,3n) - sum of exponents of primes in C(3n,2n).

%I A023987 #9 Jun 11 2025 09:14:11
%S A023987 0,1,2,0,2,4,2,3,5,4,5,2,2,7,5,5,7,7,7,3,9,11,3,5,6,8,11,7,9,12,10,10,
%T A023987 10,12,11,10,13,14,13,13,14,15,14,5,8,11,8,9,9,12,14,13,16,20,12,14,
%U A023987 17,14,19,12,17,19,17,15,15,21,20,16,19,23,16,21,21,23,22,17,22,26,24,24,26,26,24,22,23
%N A023987 Sum of exponents of primes in C(5n,3n) - sum of exponents of primes in C(3n,2n).
%H A023987 Amiram Eldar, <a href="/A023987/b023987.txt">Table of n, a(n) for n = 0..10000</a>
%F A023987 From _Amiram Eldar_, Jun 11 2025: (Start)
%F A023987 a(n) = A023847(n) - A023819(n).
%F A023987 a(n) = A022559(5*n) - 2*A022559(3*n) + A022559(n). (End)
%t A023987 a[n_] := PrimeOmega[Binomial[5*n, 3*n]] - PrimeOmega[Binomial[3*n, 2*n]]; Array[a, 100, 0] (* _Amiram Eldar_, Jun 11 2025 *)
%o A023987 (PARI) a(n) = bigomega(binomial(5*n, 3*n)) - bigomega(binomial(3*n, 2*n)); \\ _Amiram Eldar_, Jun 11 2025
%Y A023987 Cf. A001222, A022559, A023819, A023847.
%Y A023987 Cf. A023978, A023979, A023980, A023981, A023982, A023983, A023984, A023985, A023986, A023990, A023991, A023992, A023993.
%K A023987 nonn
%O A023987 0,3
%A A023987 _Clark Kimberling_
%E A023987 Name clarified, offset changed to 0 and a(0) prepended by _Amiram Eldar_, Jun 11 2025