A067695 Smallest prime factor with minimum exponent in canonical prime factorization of n, a(1)=1.

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

Offset: 1

Author

Reinhard Zumkeller, Feb 23 2002

Keywords

• nonn

Examples

			a(12) = a(2^2 * 3^1) = 3, but A020639(12) = 2;
a(36) = a(2^2 * 3^2) = 2 = A020639(36).
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A020639, A034684, A028233, A051904, A067029.

Programs

Maple

a:= n-> `if`(n=1, 1, (l-> (m-> min(map(i-> i[1], select(y->
      y[2]=m, l))))(min(map(x-> x[2], l))))(ifactors(n)[2])):
seq(a(n), n=1..80);  # Alois P. Heinz, Jan 25 2023

Mathematica

a[n_] := Module[{f = FactorInteger[n], p, e}, Min[Select[f, Last[#] == Min[f[[;;, 2]]] &][[;;, 1]]]]; a[1] = 1; Array[a, 100] (* Amiram Eldar, Sep 08 2024 *)

PARI

a(n) = if (n==1, 1, my(f=factor(n), i=vecmin(f[,2])); f[vecmin(select(x->(x==i), f[,2], 1)), 1]); \\ Michel Marcus, Jul 17 2023

Python

from sympy import factorint
def A067695(n):
    if n == 1: return 1
    f, g = map(tuple,zip(*sorted(factorint(n).items())))
    return f[g.index(min(g))] # Chai Wah Wu, Feb 07 2023