A348582 a(n) is the greatest factor among all the products A307720(k) * A307720(k+1) equal to n.

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

Offset

1,2

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 largest of them.

Links

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

Rémy Sigrist, C program for A348582

Formula

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

a(n) * A348581(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) = 3.

Prog

(C) See Links section.

Crossrefs

Cf. A307720, A307730, A348581.

Sequence in context: A095163 A033677 A116548 * A346701 A347044 A117818

Adjacent sequences: A348579 A348580 A348581 * A348583 A348584 A348585

Keyword

nonn

Author

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

Status

approved