A076403 -id:A076403 - cp's OEIS frontend

A076396 Smallest prime factor of n-th perfect power.

1, 2, 2, 3, 2, 5, 3, 2, 2, 7, 2, 3, 2, 11, 5, 2, 2, 13, 2, 2, 3, 3, 2, 17, 2, 7, 19, 2, 3, 2, 2, 23, 2, 5, 2, 3, 2, 29, 2, 31, 2, 2, 3, 2, 5, 2, 11, 37, 2, 3, 2, 41, 2, 2, 43, 2, 3, 2, 2, 3, 13, 47, 2, 7, 2, 3, 2, 2, 53, 2, 5, 5, 2, 3, 2, 3, 59, 2, 61, 2, 3, 2, 5, 2, 67, 2, 3, 2, 17, 71, 2, 73, 2, 3

Offset: 1

Reinhard Zumkeller, Oct 09 2002

nonn

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Least Prime Factor.
Eric Weisstein's World of Mathematics, Perfect Powers.

Cf. A001597, A020639, A025478, A076397, A076403.

a076396 = a020639 . a025478 -- Reinhard Zumkeller, Mar 28 2014

s[n_] := If[n == 1, 1, Module[{f = FactorInteger[n]}, If[GCD @@ f[[;;, 2]] > 1, f[[1, 1]], Nothing]]]; Array[s, 10000] (* Amiram Eldar, May 16 2025 *)

a(n) = A020639(A001597(n)).

a(n) = A020639(A025478(n)).

A076397 Largest prime factor of n-th perfect power.

Original entry on oeis.org

1, 2, 2, 3, 2, 5, 3, 2, 3, 7, 2, 3, 5, 11, 5, 2, 3, 13, 7, 3, 5, 3, 2, 17, 3, 7, 19, 5, 7, 11, 2, 23, 3, 5, 13, 3, 7, 29, 5, 31, 5, 2, 11, 17, 7, 3, 11, 37, 19, 13, 5, 41, 3, 7, 43, 11, 5, 2, 23, 3, 13, 47, 3, 7, 5, 17, 13, 7, 53, 3, 11, 5, 7, 19, 29, 5, 59, 5, 61, 31, 7, 2, 13, 11, 67, 17, 23

Offset: 1

Reinhard Zumkeller, Oct 09 2002

nonn

a(n) = A006530(A001597(n)).

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Perfect Powers.
Eric Weisstein's World of Mathematics, Greatest Prime Factor.

Cf. A025478, A076396, A076403.

a076397 = a006530 . a025478 -- Reinhard Zumkeller, Mar 28 2014

perfPQ[n_]:=GCD@@FactorInteger[n][[All,2]]>1; Join[ {1},FactorInteger[ #][[-1,1]]&/@ Select[Range[5000],perfPQ]] (* Harvey P. Dale, Sep 12 2021 *)

a(n) = A006530(A025478(n)).

cp's OEIS Frontend

A076396 Smallest prime factor of n-th perfect power.

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