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A088301 a(n) = p(n)/p(n-1), where p(n) = ( floor(n*log(n)) / Product_{j=2..pi(floor(n*log(n)))} prime(j) )!.

%I A088301 #12 Dec 19 2022 03:29:20
%S A088301 1,2,4,48,90,12,3360,18,9240,15600,756,31680,42840,59280,1848,99360,
%T A088301 6497400,2970,185136,234360,18670080,347760,421800,480480,557928,
%U A088301 55965360,70073640,857280,98960400,1157520,11880,162983520,190578024
%N A088301 a(n) = p(n)/p(n-1), where p(n) = ( floor(n*log(n))  / Product_{j=2..pi(floor(n*log(n)))} prime(j) )!.
%H A088301 G. C. Greubel, <a href="/A088301/b088301.txt">Table of n, a(n) for n = 2..1000</a>
%F A088301 a(n) = p(n)/p(n-1), where p(n) = ( floor(n*log(n))  / Product_{j=2..pi(floor(n*log(n)))} prime(j) )!.
%t A088301 p[n_]:=Factorial[Floor[n*Log[n]]]/ Product[Prime[i], {i, 2, PrimePi[Floor[n*Log[n]]]}];
%t A088301 Table[p[n]/p[n-1], {n,2,50}]
%o A088301 (Magma)
%o A088301 m:=50;
%o A088301 b:= [ #PrimesUpTo(n): n in [1..2+Floor(2*m*Log(2*m))] ];
%o A088301 f:= func< n | Factorial( Floor(n*Log(n)) )/(&*[ NthPrime(j): j in [2..b[Floor(n*Log(n))]] ]) >;
%o A088301 A088301:= func< n | n le 3 select n-1 else f(n)/f(n-1) >;
%o A088301 [A088301(n): n in [2..m]]; // _G. C. Greubel_, Dec 18 2022
%o A088301 (SageMath)
%o A088301 def p(n): return factorial( floor(n*log(n)) )/product(nth_prime(j) for j in (2..prime_pi(floor(n*log(n)))))
%o A088301 def A088301(n): return p(n)/p(n-1)
%o A088301 [A088301(n) for n in range(2,50)] # _G. C. Greubel_, Dec 18 2022
%Y A088301 Cf. A000720, A050504.
%K A088301 nonn,less
%O A088301 2,2
%A A088301 _Roger L. Bagula_, Nov 04 2003
%E A088301 Edited by _G. C. Greubel_, Dec 18 2022