A345726 a(n) = Product_{k=1..n} k^(floor(n/k)^2).

1, 2, 6, 192, 960, 4976640, 34836480, 2283043553280, 4993016251023360, 3195530400654950400000, 35150834407204454400000, 417877827219530751882239882035200000, 5432411753853899774469118466457600000, 213700126654516647665669790727613605478400000

Offset: 1

Author

Vaclav Kotesovec, Jun 25 2021

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..55

Crossrefs

Cf. A073002, A092143, A129364.

Programs

Magma

[(&*[j^(Floor(n/j))^2: j in [1..n]]): n in [1..30]]; // G. C. Greubel, Feb 05 2024

Mathematica

Table[Product[k^(Floor[n/k]^2), {k, 1, n}], {n, 1, 15}]

PARI

a(n) = prod(k=1, n, k^((n\k)^2)); \\ Michel Marcus, Jun 26 2021

SageMath

[product(j^((n//j)^2) for j in range(1,n+1)) for n in range(1,31)] # G. C. Greubel, Feb 05 2024

Formula

log(a(n)) ~ c * n^2, where c = -zeta'(2) = A073002.