A088301 - OEIS

%I #12 Dec 19 2022 03:29:20

%S 1,2,4,48,90,12,3360,18,9240,15600,756,31680,42840,59280,1848,99360,

%T 6497400,2970,185136,234360,18670080,347760,421800,480480,557928,

%U 55965360,70073640,857280,98960400,1157520,11880,162983520,190578024

%N 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 G. C. Greubel, <a href="/A088301/b088301.txt">Table of n, a(n) for n = 2..1000</a>

%F 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 p[n_]:=Factorial[Floor[n*Log[n]]]/ Product[Prime[i], {i, 2, PrimePi[Floor[n*Log[n]]]}];

%t Table[p[n]/p[n-1], {n,2,50}]

%o (Magma)

%o m:=50;

%o b:= [ #PrimesUpTo(n): n in [1..2+Floor(2*m*Log(2*m))] ];

%o f:= func< n | Factorial( Floor(n*Log(n)) )/(&*[ NthPrime(j): j in [2..b[Floor(n*Log(n))]] ]) >;

%o A088301:= func< n | n le 3 select n-1 else f(n)/f(n-1) >;

%o [A088301(n): n in [2..m]]; // _G. C. Greubel_, Dec 18 2022

%o (SageMath)

%o def p(n): return factorial( floor(n*log(n)) )/product(nth_prime(j) for j in (2..prime_pi(floor(n*log(n)))))

%o def A088301(n): return p(n)/p(n-1)

%o [A088301(n) for n in range(2,50)] # _G. C. Greubel_, Dec 18 2022

%Y Cf. A000720, A050504.

%K nonn,less

%O 2,2

%A _Roger L. Bagula_, Nov 04 2003

%E Edited by _G. C. Greubel_, Dec 18 2022