A357582 - OEIS

%I #38 Sep 12 2023 08:32:46

%S 1,2,6,30,154,1105,4788,20677,216931,858925,7105392,5546059,

%T 2018025900,1480452337,3238556831,107972737,18425956230000,4683032671,

%U 14053747110612300,160436746661,33809725025123,15260431896321667,1583855315457687090000

%N a(n) = A061300(n+1)/A061300(n).

%C It is not known if the ratios A061300(n+1)/A061300(n) are always integer, but so far (for the listed terms) they are. - _Max Alekseyev_, Sep 05 2023

%H Max Alekseyev, <a href="/A357582/b357582.txt">Table of n, a(n) for n = 0..29</a>

%e a(5) = 1105 as A061300(5+1) / A061300(5) = 61261200 / 55440 = 1105.

%t A061300[n_Integer?NonNegative] := A061300[n] = Module[{fact = n!, num = 1}, Monitor[While[Length@Divisors@num != fact, num++]; num, {n, num}]]; a[n_] := A061300[n + 1]/A061300[n]; Table[a[n], {n, 0, 4}] (* _Robert P. P. McKone_, Sep 07 2023 *)

%Y Cf. A061300.

%K nonn,hard

%O 0,2

%A _J. Lowell_, Oct 04 2022

%E a(11)-a(21) from _David A. Corneth_, Oct 05 2022

%E a(22)-a(29) from _Max Alekseyev_, Sep 05 2023