A351923 Number of ordered pairs of positive integers (s,t), s,t <= n, such that (s^t) | n.

1, 3, 4, 7, 6, 9, 8, 13, 12, 13, 12, 18, 14, 17, 18, 24, 18, 24, 20, 26, 24, 25, 24, 33, 28, 29, 32, 34, 30, 37, 32, 42, 36, 37, 38, 47, 38, 41, 42, 49, 42, 49, 44, 50, 51, 49, 48, 61, 52, 56, 54, 58, 54, 63, 58, 65, 60, 61, 60, 72, 62, 65, 69, 78, 68, 73, 68, 74, 72, 77, 72, 87, 74

Offset: 1

Author

Wesley Ivan Hurt, Feb 25 2022

Keywords

• nonn

Examples

			a(4) = 7; The 7 pairs are: (1,1), (1,2), (1,3), (1,4), (2,1), (2,2) and (4,1) since all of 1^1, 1^2, 1^3, 1^4, 2^1, 2^2 and 4^1 divide 4.
		

Crossrefs

Cf. A309891.

Programs

Maple

seq(add(padic[ordp](n,d), d in numtheory[divisors](n) minus {1}) + n, n=1..80); # Ridouane Oudra, Sep 28 2024

Formula

a(n) = Sum_{k=1..n} Sum_{i=1..n} (1 - ceiling(n/(k^i)) + floor(n/(k^i))).

a(n) = A309891(n) + n. - Ridouane Oudra, Sep 28 2024