A382964 Number of k <= n such that rad(k) divides n and g * k > n where g is the largest prime factor of n and rad = A007947.

0, 1, 1, 1, 1, 3, 1, 1, 1, 4, 1, 4, 1, 4, 3, 1, 1, 5, 1, 5, 3, 5, 1, 5, 1, 5, 1, 5, 1, 12, 1, 1, 4, 6, 3, 6, 1, 6, 4, 6, 1, 14, 1, 6, 4, 6, 1, 6, 1, 6, 4, 6, 1, 6, 3, 6, 4, 6, 1, 16, 1, 6, 4, 1, 3, 17, 1, 7, 4, 13, 1, 7, 1, 7, 4, 7, 3, 18, 1, 7, 1, 7, 1, 19, 3

Offset

1,6

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Formula

a(n) = 1 for n in A246655.

1+A001221(n) <= a(n) < A010846(n) for n in A024619.

Example

Table of select n, a(n), and numbers k in row n of A382926:
 n  a(n)    row n of A382926
--------------------------------------------------------
 6    3     3, 4, 6;
10    4     4, 5, 8, 10;
12    4     6, 8, 9, 12;
14    4     4, 7, 8, 14;
15    3     5, 9, 15;
18    5     8, 9, 12, 16, 18;
20    5     5, 8, 10, 16, 20;
21    3     7, 9, 21;
22    5     4, 8, 11, 16, 22;
24    5     9, 12, 16, 18, 24;
26    5     4, 8, 13, 16, 26;
28    5     7, 8, 14, 16, 28;
30   12     8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30.

Mathematica

(* First, run the "regs" function from A369609, then: *)
Table[Count[regs[n], _?(Function[k, AllTrue[FactorInteger[n][[All, 1]], #*k > n &]])], {n, 105}]

Crossrefs

Cf. A007947, A010846, A024619, A162306, A246655, A382926.

Sequence in context: A364096 A381958 A348028 * A375011 A059619 A098950

Adjacent sequences: A382961 A382962 A382963 * A382965 A382966 A382967

Keyword

nonn

Author

Michael De Vlieger, Apr 28 2025

Status

approved