A354090 a(n) = A007947(n)^(A051904(n) - 1), where A007947 is squarefree kernel and A051904 is minimum prime exponent.

1, 1, 1, 2, 1, 1, 1, 4, 3, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 9, 1, 1, 1, 1, 16, 1, 1, 1, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 32, 1, 1, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 1, 1, 1, 27, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 10, 1, 1, 1, 1, 1

Offset: 1

Author

Antti Karttunen, May 19 2022

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A007947, A051904, A304776.

Programs

Mathematica

a[n_] := Module[{f = FactorInteger[n], e}, e = Min[f[[;; , 2]]] - 1; f[[;; , 2]] = e; Times @@ Power @@@ f]; Array[a, 100] (* Amiram Eldar, Feb 12 2023 *)

PARI

A007947(n) = factorback(factorint(n)[, 1]);
A051904(n) = if((1==n),0,vecmin(factor(n)[, 2]));
A354090(n) = (A007947(n)^(A051904(n)-1));

PARI

a(n) = {if(n==1, 1, my(f = factor(n), e = vecmin(f[,2]) - 1); prod(i = 1, #f~, f[i,1]^e));} \\ Amiram Eldar, Feb 12 2023

Formula

a(n) = A007947(n)^(A051904(n)-1).

a(n) = n / A304776(n).