The number of numbers i such that p = i (mod n) for some powerful number p and 0 <= i < n.

1, 2, 3, 3, 5, 6, 7, 6, 7, 10, 11, 9, 13, 14, 15, 12, 17, 14, 19, 15, 21, 22, 23, 18, 21, 26, 21, 21, 29, 30, 31, 24, 33, 34, 35, 21, 37, 38, 39, 30, 41, 42, 43, 33, 35, 46, 47, 36, 43, 42, 51, 39, 53, 42, 55, 42, 57, 58, 59, 45, 61, 62, 49, 48, 65, 66, 67, 51

1

Inspired by a recent paper by Chen.

T. D. Noe, Plot of 200 terms

T. D. Noe, Table of 200 terms

Tsz Ho Chan, Squarefull numbers in arithmetic progression II, arXiv 1407.0054, Jun 30 2014

(Mma) nn = 8; nMax = 10^nn; lst = {}; Do[lst = Join[lst, i^3 Range[Sqrt[nMax/i^3]]^2], {i, nMax^(1/3)}]; Table[Length[Complement[Range[0, n - 1], Transpose[Tally[Mod[lst, n]]][[1]]]], {n, 200}]

Cf. A001694 (powerful), A005117 (squarefree), A013929 (not squarefree), S000120, S000121.

nonn

T. D. Noe, Jul 03 2014