A337771 Number of positive integer pairs, (s,t), with s,t composite, such that s < t < n, and neither s nor t divides n.

0, 0, 0, 0, 0, 0, 1, 0, 3, 6, 10, 3, 15, 15, 21, 15, 36, 21, 45, 28, 55, 66, 78, 36, 91, 105, 105, 105, 153, 105, 171, 120, 190, 210, 231, 153, 276, 276, 300, 231, 351, 276, 378, 325, 351, 435, 465, 300, 496, 465, 561, 528, 630, 496, 666, 561, 741, 780, 820, 561, 861, 861

Offset

1,9

Links

Table of n, a(n) for n=1..62.

Formula

a(n) = Sum_{k=1..n} Sum_{i=1..k-1} c(i) * c(k) * (ceiling(n/i) - floor(n/i)) * (ceiling(n/k) - floor(n/k)), where c is the characteristic function of composite numbers (A066247).

Example

a(10) = 6; There are 6 positive integer pairs, (s,t), with s,t composite, such that s < t < n, and neither s nor t divides 10. The composite numbers less than 10 that do not divide 10 are {4,6,8,9}. The positive integer pairs are (4,6), (4,8), (4,9), (6,8), (6,9), and (8,9).

Mathematica

Table[Sum[Sum[(1 - PrimePi[i] + PrimePi[i - 1]) (1 - PrimePi[k] + PrimePi[k - 1]) (Ceiling[n/k] - Floor[n/k]) (Ceiling[n/i] - Floor[n/i]), {i, 2, k - 1}], {k, n}], {n, 80}]

Crossrefs

Cf. A066247.

Sequence in context: A120028 A333611 A329153 * A232175 A065234 A333531

Adjacent sequences: A337768 A337769 A337770 * A337772 A337773 A337774

Keyword

nonn

Author

Wesley Ivan Hurt, Sep 19 2020

Status

approved