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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, 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
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
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Sep 19 2020
STATUS
approved