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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).
2
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
1,4
COMMENTS
This sequence contains nonzero values in A355432.
LINKS
Michael De Vlieger, Scatterplot of a(n), n = 1..2^16, highlighting records (A360768(n) in A360589) in red.
FORMULA
a(n) = A355432(A360768(n)) = length of row n in A359929.
EXAMPLE
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
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]
KEYWORD
nonn
AUTHOR
Michael De Vlieger, Mar 29 2023
STATUS
approved