A393580 a(n) is the largest m <= A002034(n) such that n divides m * ... * A002034(n).

1, 2, 3, 4, 5, 2, 7, 2, 3, 4, 11, 3, 13, 6, 3, 2, 17, 3, 19, 4, 6, 10, 23, 2, 5, 12, 6, 4, 29, 3, 31, 4, 9, 16, 5, 3, 37, 18, 12, 2, 41, 6, 43, 8, 3, 22, 47, 2, 7, 5, 15, 12, 53, 6, 10, 4, 18, 28, 59, 3, 61, 30, 3, 4, 10, 9, 67, 16, 21, 5, 71, 3, 73, 36, 5, 16

Offset

1,2

Comments

We know that n divides 1 * 2 * ... * A002034(n); here we narrow this product.

Links

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

Example

The first terms are:
  n   a(n)  A002034(n)
  --  ----  ----------
   1     1           1
   2     2           2
   3     3           3
   4     4           4
   5     5           5
   6     2           3
   7     7           7
   8     2           4
   9     3           6
  10     4           5
  11    11          11
  12     3           4
  13    13          13
  14     6           7
  15     3           5
  16     2           6

Prog

(PARI) a(n) = { my (r = n); for (k = 1, oo, r /= gcd(r, k); if (r==1, r = n; forstep (m = k, -oo, -1, r /= gcd(r, m); if (r==1, return (m); ); ); ); ); }

Crossrefs

Cf. A002034.

Sequence in context: A386630 A308201 A026362 * A223490 A354749 A244734

Adjacent sequences: A393577 A393578 A393579 * A393581 A393582 A393583

Keyword

nonn

Author

Rémy Sigrist, Feb 22 2026

Status

approved