A390599 Smallest number obtained by concatenating a permutation of the divisors of n.

1, 12, 13, 124, 15, 1236, 17, 1248, 139, 10125, 111, 1122346, 113, 11427, 11535, 116248, 117, 1182369, 119, 10120245, 12137, 111222, 123, 1122243468, 1255, 113226, 12739, 11422847, 129, 10115230356, 131, 11623248, 111333, 117234, 13557, 112182336469, 137, 119238

Offset

1,2

Links

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

Edvard Davtyan and Lewin Gan, 632C - The Smallest String Concatenation, Tutorial, Educational Codeforces Round 9.

Mathematica

a[n_]:=Min[FromDigits/@Flatten/@IntegerDigits/@Permutations[Divisors[n]]]; Array[a, 38] (* James C. McMahon, Nov 13 2025 *)

Prog

(PARI) a(n) = {my(d=apply(x->Str(x), divisors(n)), d2=vecsort(d, (x, y)->cmp(concat(x, y), concat(y, x)))); eval(concat(d2))}
(Python)
from sympy import divisors
from functools import cmp_to_key
def c(x, y): return -1 if x+y < y+x else int(x+y > y+x)
def a(n): return int("".join(sorted(list(map(str, divisors(n))), key=cmp_to_key(c))))
print([a(n) for n in range(1, 39)]) # Michael S. Branicky, Nov 12 2025

Crossrefs

Cf. A037278, A060555.

Sequence in context: A135123 A129476 A243361 * A037278 A164852 A362113

Adjacent sequences: A390596 A390597 A390598 * A390600 A390601 A390602

Keyword

nonn,base,easy

Author

Jason Yuen, Nov 12 2025

Status

approved