A359612 - OEIS

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A359612

Largest prime factor with minimal exponent in canonical prime factorization of n.

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

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OFFSET

2,1

COMMENTS

When inspecting the minimal exponent of the canonical representation of n, a(n) is the largest of those primes, while A067695(n) is the smallest.

On the other hand if the maximal exponent is regarded similarly, A356840(n) is the largest of those primes and A356838(n) is the smallest.

18 is the smallest n, where a(n) differs from A006530(n), since a(18) = 2, while A006530(18) = 3.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 2..20000

EXAMPLE

a(162) = a(2^1 * 3^4) = 2.

a(225) = a(3^2 * 5^2) = 5.

MAPLE

a:= n-> (l-> (m-> max(map(i-> i[1], select(y->y[2]=m,

l))))(min(map(x-> x[2], l))))(ifactors(n)[2]):

seq(a(n), n=2..75); # Alois P. Heinz, Jan 25 2023

MATHEMATICA

a[n_] := Module[{f = FactorInteger[n], e, ind}, e = f[[;; , 2]]; ind = Position[e, Min[e]][[-1, 1]]; f[[ind, 1]]]; Array[a, 100, 2] (* Amiram Eldar, Jan 07 2023 *)

PROG

(Python)

from sympy import factorint

def a(n):

max_factor = 0

min_exponent = float("inf")

for p, exponent in factorint(n).items():

if exponent < min_exponent:

max_factor = p

min_exponent = exponent

elif exponent == min_exponent:

max_factor = max(max_factor, p)

return max_factor

(Python)

from sympy import factorint

def A359612(n): return (f:=list(map(tuple, zip(*sorted(factorint(n).items(), reverse=True)))))[0][f[1].index(min(f[1]))] # Chai Wah Wu, Feb 07 2023

(PARI) a(n) = my(f=factor(n), e=vecmin(f[, 2])); f[vecmax(select(x->(x==e), f[, 2], 1)), 1]; \\ Michel Marcus, Jan 26 2023

CROSSREFS

Cf. A006530, A067695, A356838, A356840.

Sequence in context: A197861 A180506 A273283 * A276440 A162325 A324371

Adjacent sequences: A359609 A359610 A359611 * A359613 A359614 A359615

KEYWORD

nonn

AUTHOR

Jens Ahlström, Jan 06 2023

STATUS

approved