A343750 Let S be the set of all numbers that can be obtained by permuting the digits of n (leading zeros can be omitted). Then a(n) is that element of S with the smallest number of divisors. In case of a tie, choose the smallest.

1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 11, 21, 13, 41, 15, 61, 17, 81, 19, 2, 21, 22, 23, 24, 25, 26, 27, 82, 29, 3, 13, 23, 33, 43, 53, 63, 37, 83, 39, 4, 41, 24, 43, 44, 45, 46, 47, 48, 49, 5, 15, 25, 53, 45, 55, 65, 57, 58, 59, 6, 61, 26, 63, 46, 65

Offset

1,2

Comments

a(x0..0) = x, a(x..x) = x..x, x from {1,...,9}.

Links

Table of n, a(n) for n=1..65.

Example

n = 125, S = {125, 152, 215, 251, 512, 521}. The elements 251 and 521 have the smallest number of divisors which equals 2. The smallest from elements 251 and 521 is 251, thus a(125) = 251.

Mathematica

a[n_] := Module[{perm  = FromDigits /@ Permutations[IntegerDigits[n]], d}, d = DivisorSigma[0, perm]; Min @ perm[[Position[d, Min[d]] // Flatten]]]; Array[a, 65] (* Amiram Eldar, Apr 27 2021 *)

Crossrefs

Cf. A000005, A272215.

Sequence in context: A004719 A004151 A151765 * A107603 A161594 A084011

Adjacent sequences: A343747 A343748 A343749 * A343751 A343752 A343753

Keyword

nonn,base

Author

Ctibor O. Zizka, Apr 27 2021

Status

approved