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A309912 a(n) = Product_{p prime, p <= n} floor(n/p).

%I A309912 #13 Jun 02 2025 13:21:03
%S A309912 1,1,1,1,2,2,6,6,8,12,30,30,48,48,112,210,240,240,324,324,480,840,
%T A309912 1848,1848,2304,2880,6240,7020,10080,10080,14400,14400,15360,25344,
%U A309912 53856,78540,90720,90720,191520,311220,374400,374400,508032,508032,709632,855360,1788480,1788480
%N A309912 a(n) = Product_{p prime, p <= n} floor(n/p).
%C A309912 Product of exponents of prime factorization of A048803 (squarefree factorials).
%F A309912 a(n) = Product_{k=1..A000720(n)} floor(n/A000040(k)).
%F A309912 a(n) = A005361(A048803(n)).
%e A309912 A048803(14) = 1816214400 = 2^7 * 3^4 * 5^2 * 7^2 * 11 * 13 so a(14) = 7 * 4 * 2 * 2 * 1 * 1 = 112.
%p A309912 a:= n-> mul(floor(n/p), p=select(isprime, [$2..n])):
%p A309912 seq(a(n), n=0..50);  # _Alois P. Heinz_, Aug 23 2019
%t A309912 Table[Product[Floor[n/Prime[k]], {k, 1, PrimePi[n]}], {n, 0, 47}]
%o A309912 (Python)
%o A309912 from math import prod
%o A309912 from sympy import primerange
%o A309912 def A309912(n): return prod(n//p for p in primerange(n)) # _Chai Wah Wu_, Jun 02 2025
%Y A309912 Cf. A000040, A000720, A005361, A010786, A013939, A048803, A135291.
%K A309912 nonn
%O A309912 0,5
%A A309912 _Ilya Gutkovskiy_, Aug 22 2019