A357241 a(n) is the number of j in the range 1 <= j <= n such that j / rad(j) = n / rad(n).

1, 2, 3, 1, 4, 5, 6, 1, 1, 7, 8, 2, 9, 10, 11, 1, 12, 2, 13, 3, 14, 15, 16, 2, 1, 17, 1, 4, 18, 19, 20, 1, 21, 22, 23, 1, 24, 25, 26, 3, 27, 28, 29, 5, 3, 30, 31, 2, 1, 2, 32, 6, 33, 2, 34, 4, 35, 36, 37, 7, 38, 39, 4, 1, 40, 41, 42, 8, 43, 44, 45, 1, 46, 47, 3, 9, 48, 49, 50, 3

Offset: 1

Author

Ilya Gutkovskiy, Sep 19 2022

Keywords

• nonn

Links

• Michel Marcus, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001694 (positions of 1's), A003557, A008479.

Programs

Mathematica

Table[Length[Select[Range[n], #/Last[Select[Divisors[#], SquareFreeQ]] == n/Last[Select[Divisors[n], SquareFreeQ]] &]], {n, 1, 80}]

PARI

f(n) = n/factorback(factor(n)[, 1]); \\ A003557
a(n) = my(x=f(n)); sum(j=1, n, f(j) == x); \\ Michel Marcus, Sep 20 2022

Formula

a(n) = |{j <= n : A003557(j) = A003557(n)}|.