A056690 a(n) = floor(product_{k=2..n} log(k)).
0, 0, 1, 1, 3, 5, 12, 27, 62, 149, 371, 952, 2513, 6807, 18873, 53472, 154554, 455076, 1363287, 4150560, 12829558, 40227005, 127843589, 411512640, 1340747909, 4418886387, 14724633149, 49582195801, 168638834537, 579103599979
Offset: 2
Examples
log(2)*log(3)*log(4)*log(5)= 1.699... So a(5) = 1, since the integer part of 1.699... is 1.
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 2..1000
Programs
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Mathematica
Table[Floor[Product[Log[k], {k, 2, n}]], {n, 2, 40}] (* Vaclav Kotesovec, Nov 28 2015 *)
Formula
log(a(n)) ~ n*(log(log(n)) - 1/log(n) - 1/log(n)^2 - 2/log(n)^3 - 6/log(n)^4 - 24/log(n)^5 - ...). - Vaclav Kotesovec, Feb 12 2023