A392843 a(n) is the least divisor d of n such that n is the product of distinct elements of 1..d.

1, 2, 3, 4, 5, 3, 7, 4, 9, 5, 11, 4, 13, 7, 5, 8, 17, 6, 19, 5, 7, 11, 23, 4, 25, 13, 9, 7, 29, 5, 31, 8, 11, 17, 7, 6, 37, 19, 13, 5, 41, 7, 43, 11, 9, 23, 47, 6, 49, 10, 17, 13, 53, 9, 11, 7, 19, 29, 59, 5, 61, 31, 9, 8, 13, 11, 67, 17, 23, 7, 71, 6, 73, 37

Offset

1,2

Comments

This sequence diverges.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Formula

a(n!) = n for any n >= 1.

n <= a(n)!.

a(n) <= n with equality iff n belongs to A166684.

a(n) >= A002034(n).

Example

The first terms, alongside appropriate products, are:
  n   a(n)  Product
  --  ----  -------
   1     1  1
   2     2  2
   3     3  3
   4     4  4
   5     5  5
   6     3  2 * 3
   7     7  7
   8     4  2 * 4
   9     9  9
  10     5  2 * 5
  11    11  11
  12     4  3 * 4
  13    13  13
  14     7  2 * 7
  15     5  3 * 5
  16     8  2 * 8

Prog

(PARI) a(n) = { my (p = [1]); fordiv (n, d, p = setunion(p, select(v -> v <= n, d*p)); if (p[#p]==n, return (d); ); ); }

Crossrefs

Cf. A002034, A166684.

Sequence in context: A248937 A088491 A353172 * A140271 A223491 A346088

Adjacent sequences: A392840 A392841 A392842 * A392844 A392845 A392846

Keyword

nonn

Author

Rémy Sigrist, Feb 21 2026

Status

approved