A092593 a(n) is the smallest number k > 1 for which A001142(k)/A002944(k+1)^n is an integer.

2, 3, 9, 9, 15, 15, 38, 45, 45, 45, 61, 61, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 635, 635, 1545, 1545, 1545, 1545, 2137, 2137, 2137, 2137, 2137, 2137, 2137, 2137, 2660, 2660, 2660, 2660, 2660, 2660, 2660, 2660, 2660, 2660, 2660, 2660, 2660, 2660, 2660, 2660, 2660, 2660, 2660, 2660, 2660, 2660, 2660, 2660, 2660

Offset: 1

Author

Labos Elemer, Mar 10 2004

Keywords

• nonn

Comments

a(62) > 12500. - Robert Israel, Jan 24 2019

Examples

			n=4, A001142(9) = 1*9*36*...*9*1 = 11759522374656,
A002944(10) = lcm(1,2,...,10)/10=252 and A001142(9) = 2916*(252^4) = 11759522374656,
so a(4)=9, the smallest relevant number.
		

Crossrefs

Cf. A001142, A002944, A092593.

Programs

Maple

A001142:= proc(n) option remember; procname(n-1)*n^(n-1)/(n-1)! end proc:
A001142(0):= 1:
A002944:= proc(n) option remember; ilcm(n,procname(n-1)*(n-1))/n end proc:
A002944(1):= 1:
f:= proc(n) option remember; local k;
for k from procname(n-1) do
   if type(A001142(k)/A002944(k+1)^n, integer) then return k fi
od
end proc:
f(1):= 2:
map(f, [$1..61]); # Robert Israel, Jan 23 2019

Mathematica

Table[fla=1;Do[s1=Apply[Times, Table[Binomial[n, j], {j, 0, n}]]; s2=Apply[LCM, Table[Binomial[n, j], {j, 0, n}]]; If[IntegerQ[s1/(s2^k)]&&!Equal[n, 1]&&Equal[fla, 1], Print[{n, k}];fla=0], {n, 1, 230}], {k, 1, 25}]

Extensions

Corrected and extended by Robert Israel, Jan 23 2019