A337683 Number of distinct positive integer pairs, (s,t), with s < t < n such that neither s nor t divides n and the harmonic mean of s and t is an integer.
0, 0, 0, 0, 0, 0, 2, 1, 1, 1, 2, 0, 4, 3, 3, 4, 6, 2, 8, 5, 8, 9, 10, 3, 11, 11, 9, 10, 14, 7, 18, 14, 16, 17, 17, 9, 22, 21, 20, 13, 24, 16, 28, 25, 21, 31, 32, 19, 33, 28, 32, 31, 34, 25, 34, 28, 36, 37, 38, 17, 44, 43, 37, 40, 44, 40, 50, 47, 48, 39, 52, 28, 56, 55, 48, 55
Offset: 1
Examples
a(7) = 2; There are 2 distinct positive integer pairs, (s,t), with s < t < 7 such that neither s nor t divides 7 and the harmonic mean of s and t is an integer. They are (2,6) and (3,6).
Programs
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Mathematica
Table[Sum[Sum[(1 - Ceiling[2 (i*k)/(k + i)] + Floor[2 (i*k)/(k + i)]) (Ceiling[n/k] - Floor[n/k]) (Ceiling[n/i] - Floor[n/i]), {i, k - 1}], {k, n}], {n, 100}]
Formula
a(n) = Sum_{k=1..n} Sum_{i=1..k-1} (ceiling(n/k) - floor(n/k)) * (ceiling(n/i) - floor(n/i)) * (1 - ceiling(2*(k*i)/(k+i)) + floor(2*(k*i)/(k+i))).