A339146 a(n) = a(floor(n / 5)) * (n mod 5 + 1); initial terms are 1.

1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 2, 4, 6, 8, 10, 3, 6, 9, 12, 15, 4, 8, 12, 16, 20, 5, 10, 15, 20, 25, 1, 2, 3, 4, 5, 2, 4, 6, 8, 10, 3, 6, 9, 12, 15, 4, 8, 12, 16, 20, 5, 10, 15, 20, 25, 1, 2, 3, 4, 5, 2, 4, 6, 8, 10, 3, 6, 9, 12, 15, 4, 8, 12, 16, 20, 5, 10, 15, 20, 25

Offset: 0

Author

Robert Dougherty-Bliss, Nov 25 2020

Keywords

• nonn

Comments

If a(n) is arranged in a table with row lengths 5, then the first column is the transpose of the first row, followed the transpose of the second row, followed by the transpose of the third row, and so on. The remainder of each row (except the first) is an arithmetic progression whose start and step size equals the first entry of the row.

a(n) = O(n).

limsup_n a(n) = +oo.

Examples

			a(10) = a(2) * 1 = 1.
a(13) = a(2) * 4 = 4.
		

Crossrefs

Cf. A194459.

Cf. A048896 (with 2 instead of 5, but shifted).

Programs

PARI

a(n) = if (n < 5, 1, a(n\5)*(n % 5 + 1)); \\ Michel Marcus, Nov 26 2020

Python

def a(n):
    if n < 5:
        return 1
    q, r = divmod(n, 5)
    return a(q) * (r + 1)