A390052 a(1) = 1. For n > 1, a(n) is the smallest number obtainable by rearranging the digits of n whose value has the largest prime factor among all such rearrangements.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 21, 31, 41, 51, 61, 71, 18, 19, 20, 21, 22, 23, 42, 52, 62, 27, 82, 29, 30, 31, 23, 33, 43, 53, 63, 73, 83, 93, 40, 41, 42, 43, 44, 45, 46, 47, 84, 94, 5, 51, 52, 53, 45, 55, 65, 57, 58, 59, 60, 61, 62, 63, 46, 65, 66, 67, 86, 69

Offset

1,2

Comments

Any leading zeros of a rearrangement are discarded.

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Example

a(153) = 531 since the digits of 153 can be rearranged to 135,315,351,513 and 531; and 531 has the largest prime factor of the set (59).

Mathematica

A390052[n_] := Last[SortBy[Map[FromDigits, Permutations[IntegerDigits[n]]], FactorInteger[#][[-1, 1]] &, Less]];
Array[A390052, 100] (* Paolo Xausa, Oct 31 2025 *)

Prog

(Python)
from sympy import factorint
from itertools import permutations
def a(n):
    if n == 1: return 1
    m, argm = 0, None
    for p in permutations(sorted(str(n))):
        t = int("".join(p))
        f = 0 if t == 1 else max(factorint(t))
        if f > m: m, argm = f, t
    return argm
print([a(n) for n in range(1, 70)])
(PARI) gpf(n) = if (n==1, 1, vecmax(factor(n)[, 1]));
a(n) = my(d = digits(n), vi = vecsort(vector((#d)!, i, my(p = numtoperm(#d, i-1)); fromdigits(vector(#d, k, d[p[k]])))), vg = apply(gpf, vi), vmax = vecmax(vg), vs = select(x->(x==vmax), vg, 1)); vi[vs[1]]; \\ Michel Marcus, Oct 24 2025

Crossrefs

Cf. A006530, A390053, A387938 (fixed points).

Sequence in context: A378808 A064222 A261294 * A321474 A333659 A336956

Adjacent sequences: A390049 A390050 A390051 * A390053 A390054 A390055

Keyword

nonn,base,look

Author

Michael S. Branicky and Ali Sada, Oct 22 2025

Status

approved