A111260 Numbers of the form (m^n)/(n^m) with m > 0 and n>1.
1, 4, 16, 27, 256, 729, 65536, 2985984, 4194304, 9765625, 134217728, 387420489, 2176782336, 24794911296, 30517578125, 104857600000, 678223072849, 2641807540224, 7625597484987, 17592186044416, 281474976710656
Offset: 1
Keywords
Examples
The 4th element is a=27 with m = 3 and n = 9 because 3^9/9^3 = 27.
Programs
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Maple
a:=proc(N) local a, m,n; for m from 1 to N do for n from 2 to N do a:=(m^n)/(n^m); if(floor(a)=a)then print(a) fi; od; od; end: # convert into set # sort set
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Mathematica
Take[ Select[ Union@Flatten@Table[(m^n)/(n^m), {m, 35}, {n, 2, 35}], IntegerQ[ # ] &], 21] (* Robert G. Wilson v, Nov 17 2005 *)