A076405 Next perfect power having the same least root of n-th perfect power, A001597.

1, 8, 16, 27, 32, 125, 81, 64, 216, 343, 128, 243, 1000, 1331, 625, 256, 1728, 2197, 2744, 1296, 3375, 729, 512, 4913, 5832, 2401, 6859, 8000, 9261, 10648, 1024, 12167, 13824, 3125, 17576, 2187, 21952, 24389, 27000, 29791, 10000, 2048, 35937, 39304

Offset

1,2

Comments

A025478(a(n)) = A025478(n); A001597(a(n)) = A025478(n)*A001597(n).

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Perfect Powers.

Example

.   n  | A001597(n) | A025478(n)^A025479(n) |  a(n)
. -----+------------+-----------------------+---------------------------
.  13  |       100  |         10^2          | 1000 = 10^3 = A001597(41)
.  14  |       121  |         11^2          | 1331 = 11^3 = A001597(47)
.  15  |       125  |          5^3          |  625 =  5^4 = A001597(34)
.  16  |       128  |          2^7          |  256 =  2^8 = A001597(23)
.  17  |       144  |         12^2          | 1728 = 12^3 = A001597(54).

Mathematica

ppQ[n_] := GCD @@ Last /@ FactorInteger@# > 1; f[n_] := Block[{fi = Transpose@ FactorInteger@ n}, fi2 = fi[[2]]; Times @@ (fi[[1]]^(fi[[2]] (1 + 1/GCD @@ fi[[2]])))]; lst = Join[{1}, Select[ Range@ 1848, ppQ@# &]]; f /@ lst (* Robert G. Wilson v, Aug 03 2008 *)

Prog

(Haskell)
a076405 n = a076405_list !! (n-1)
a076405_list = 1 : f (tail $ zip a001597_list a025478_list) where
   f ((p, r) : us) = g us where
     g ((q, r') : vs) = if r' == r then q : f us else g vs
-- Reinhard Zumkeller, Mar 11 2014

Crossrefs

Cf. A052410.

Sequence in context: A111231 A111307 A246549 * A099997 A053093 A175086

Adjacent sequences: A076402 A076403 A076404 * A076406 A076407 A076408

Keyword

nonn

Author

Reinhard Zumkeller, Oct 09 2002

Extensions

More terms from Robert G. Wilson v, Aug 03 2008

Status

approved