A348581 a(n) is the least factor among all the products A307720(k) * A307720(k+1) equal to n.

1, 1, 1, 2, 1, 2, 1, 2, 3, 2, 1, 3, 1, 2, 3, 2, 1, 3, 1, 4, 3, 2, 1, 3, 5, 2, 3, 4, 1, 5, 1, 4, 3, 2, 5, 4, 1, 2, 3, 5, 1, 6, 1, 4, 5, 2, 1, 6, 7, 5, 3, 4, 1, 6, 5, 7, 3, 2, 1, 6, 1, 2, 7, 8, 5, 6, 1, 4, 3, 7, 1, 8, 1, 2, 5, 4, 7, 6, 1, 8, 9, 2, 1, 7, 5, 2, 3

Offset

1,4

Comments

We know there are n ways to get n as a product of terms A307720(k)*A307720(k+1) for various k's. Look at these 2*n numbers from A307720. Then a(n) is the smallest of them.

Links

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

Rémy Sigrist, C program for A348581

Formula

a(p) = 1 for any prime number p.

a(n) * A348582(n) = n.

Example

For n = 6:
- we have the following products equal to 6:
    A307720(7)  * A307720(8)  = 3 * 2 = 6
    A307720(12) * A307720(13) = 2 * 3 = 6
    A307720(13) * A307720(14) = 3 * 2 = 6
    A307720(14) * A307720(15) = 2 * 3 = 6
    A307720(15) * A307720(16) = 3 * 2 = 6
    A307720(16) * A307720(17) = 2 * 3 = 6
- the corresponding distinct factors are 2 and 3,
- hence a(6) = 2.

Prog

(C) See Links section.

Crossrefs

Cf. A307720, A307730, A348582.

Sequence in context: A345266 A217581 A366521 * A124044 A059981 A033676

Adjacent sequences: A348578 A348579 A348580 * A348582 A348583 A348584

Keyword

nonn

Author

Rémy Sigrist and N. J. A. Sloane, Oct 24 2021

Status

approved