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

Author

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

Keywords

• nonn

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.

Examples

			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.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, C program for A348581

Crossrefs

Cf. A307720, A307730, A348582.

Programs

C

See Links section.

Formula

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

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