Number of composite numbers in the range implied by S000568(n).
0, 1, 3, 5, 7, 9, 13, 11, 11, 13, 17, 17, 21, 19, 23, 23, 25, 29, 29, 29, 33, 33, 35, 39, 41, 39, 43, 43, 47, 57, 49, 51, 51, 53, 53, 59, 57, 61, 59, 71, 63, 67, 69, 67, 69, 75, 77, 77, 81, 81, 83, 85, 83, 85, 87, 89, 95, 95, 99, 99, 97, 103, 105, 99, 105, 109
0
The graph is fairly linear, with a slope of about 1.6.
T. D. Noe, Plot of 101 terms
T. D. Noe, Table of 101 terms
Eric W. Weisstein, MathWorld: Squarefree
(Mma) nn = 50; sf = Table[0, {nn}]; found = 0; n = 1; While[found < nn, n++; c = Count[Table[SquareFreeQ[i], {i, Prime[n] + 1, Prime[n + 1] - 1}], True]; If[0 < c <= nn && sf[[c]] == 0, sf[[c]] = n; found++]]; t =Join[{2}, Prime[sf]]; Table[NextPrime[p] - p - 1, {p, t}]
Cf. S000568.
nonn,hard
T. D. Noe, Apr 10 2015