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

1,4

Links

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

Formula

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

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

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 *)

Prog

(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

Crossrefs

Cf. A007947, A051904, A304776.

Sequence in context: A337087 A321312 A327502 * A362826 A220632 A125653

Adjacent sequences: A354087 A354088 A354089 * A354091 A354092 A354093

Keyword

nonn

Author

Antti Karttunen, May 19 2022

Status

approved