A076397 -id:A076397 - 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)).

A122444 Greatest prime factor of powers of semiprimes.

Original entry on oeis.org

1, 2, 3, 3, 5, 7, 5, 2, 7, 11, 5, 13, 11, 17, 7, 3, 19, 13, 23, 7, 17, 11, 19, 29, 31, 2, 13, 23, 37, 11, 3, 41, 17, 43, 29, 13, 31, 47, 19, 5, 53, 37, 23, 59, 17, 11, 61, 41, 43, 19, 67, 47, 71, 13, 29, 73, 31, 79, 53, 23, 83

Offset: 1

Jonathan Vos Post, Sep 06 2006

A122443 is least prime factor of powers of semiprimes. Cf. A076397 Largest prime factor of n-th perfect power.

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Cf. A000040, A001358, A006530, A020639, A076396, A076397, A085155, A122443.

FactorInteger[#][[-1, 1]] & /@ Select[Range@ 168, Function[n, Or[n == 1, And[Length@ # == 1, EvenQ@ First@ #], And[Length@ # == 2, SameQ @@ #]] &[FactorInteger[n][[All, -1]]]]] (* Michael De Vlieger, Mar 04 2017 *)

a(n) = A006530(A085155(n)) = greatest prime factor of A085155 powers of semiprimes.

cp's OEIS Frontend

A076396 Smallest prime factor of n-th perfect power.

Views

Author

Keywords

Links

Crossrefs

Programs

Haskell

Mathematica

Formula