A359382 a(n) = number of k < t such that rad(k) = rad(t) and k does not divide t, where t = A360768(n) and rad(k) = A007947(k).

1, 1, 1, 2, 2, 4, 2, 1, 1, 1, 4, 2, 2, 4, 1, 1, 1, 1, 3, 1, 3, 2, 8, 1, 2, 1, 7, 2, 1, 2, 5, 2, 1, 1, 3, 3, 1, 6, 1, 1, 5, 5, 4, 5, 1, 1, 4, 8, 3, 3, 1, 2, 1, 4, 2, 3, 5, 10, 2, 1, 3, 3, 1, 1, 1, 6, 1, 3, 7, 1, 1, 7, 3, 14, 3, 6, 3, 2, 1, 1, 2, 7, 2, 1, 1, 2, 2, 8, 4, 6, 4, 8, 1, 1, 2, 1, 6, 9, 2, 1

Offset: 1

Author

Michael De Vlieger, Mar 29 2023

Keywords

• nonn

Comments

This sequence contains nonzero values in A355432.

Examples

			Table relating a(n) to b(n) = A360768(n) and row n of A359929.
n  b(n)   row n of A359929   a(n)
---------------------------------
1   18    12                   1
2   24    18                   1
3   36    24                   1
4   48    18, 36               2
5   50    20, 40               2
6   54    12, 24, 36, 48       4
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000
• Michael De Vlieger, Scatterplot of a(n), n = 1..2^16, highlighting records (A360768(n) in A360589) in red.

Crossrefs

Cf. A007947, A010846, A013929, A020639, A024619, A027750, A126706, A162306, A243822, A272618, A355432, A359929, A360589, A360768.

Programs

Mathematica

rad[x_] := rad[x] = Times @@ FactorInteger[x][[All, 1]];
s = Select[Range[671], Nor[SquareFreeQ[#], PrimePowerQ[#]] &];
t = Select[s, #1/#2 >= #3 & @@ {#1, Times @@ #2, #2[[2]]} & @@
      {#, FactorInteger[#][[All, 1]]} &];
Map[Function[{n, k},
    Count[TakeWhile[s, # < n &],
      _?(And[rad[#] == k, ! Divisible[n, #]] &)]] @@ {#, rad[#]} &, t]

Formula

a(n) = A355432(A360768(n)) = length of row n in A359929.