A359382 - OEIS

%I #16 Apr 01 2023 13:29:08

%S 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,

%T 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,

%U 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

%N 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).

%C This sequence contains nonzero values in A355432.

%H Michael De Vlieger, <a href="/A359382/b359382.txt">Table of n, a(n) for n = 1..10000</a>

%H Michael De Vlieger, <a href="/A359382/a359382.png">Scatterplot of a(n)</a>, n = 1..2^16, highlighting records (A360768(n) in A360589) in red.

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

%e Table relating a(n) to b(n) = A360768(n) and row n of A359929.

%e n  b(n)   row n of A359929   a(n)

%e ---------------------------------

%e 1   18    12                   1

%e 2   24    18                   1

%e 3   36    24                   1

%e 4   48    18, 36               2

%e 5   50    20, 40               2

%e 6   54    12, 24, 36, 48       4

%t rad[x_] := rad[x] = Times @@ FactorInteger[x][[All, 1]];

%t s = Select[Range[671], Nor[SquareFreeQ[#], PrimePowerQ[#]] &];

%t t = Select[s, #1/#2 >= #3 & @@ {#1, Times @@ #2, #2[[2]]} & @@

%t       {#, FactorInteger[#][[All, 1]]} &];

%t Map[Function[{n, k},

%t     Count[TakeWhile[s, # < n &],

%t       _?(And[rad[#] == k, ! Divisible[n, #]] &)]] @@ {#, rad[#]} &, t]

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

%K nonn

%O 1,4

%A _Michael De Vlieger_, Mar 29 2023