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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).

%I A359382 #16 Apr 01 2023 13:29:08
%S A359382 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 A359382 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 A359382 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 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).
%C A359382 This sequence contains nonzero values in A355432.
%H A359382 Michael De Vlieger, <a href="/A359382/b359382.txt">Table of n, a(n) for n = 1..10000</a>
%H A359382 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 A359382 a(n) = A355432(A360768(n)) = length of row n in A359929.
%e A359382 Table relating a(n) to b(n) = A360768(n) and row n of A359929.
%e A359382 n  b(n)   row n of A359929   a(n)
%e A359382 ---------------------------------
%e A359382 1   18    12                   1
%e A359382 2   24    18                   1
%e A359382 3   36    24                   1
%e A359382 4   48    18, 36               2
%e A359382 5   50    20, 40               2
%e A359382 6   54    12, 24, 36, 48       4
%t A359382 rad[x_] := rad[x] = Times @@ FactorInteger[x][[All, 1]];
%t A359382 s = Select[Range[671], Nor[SquareFreeQ[#], PrimePowerQ[#]] &];
%t A359382 t = Select[s, #1/#2 >= #3 & @@ {#1, Times @@ #2, #2[[2]]} & @@
%t A359382       {#, FactorInteger[#][[All, 1]]} &];
%t A359382 Map[Function[{n, k},
%t A359382     Count[TakeWhile[s, # < n &],
%t A359382       _?(And[rad[#] == k, ! Divisible[n, #]] &)]] @@ {#, rad[#]} &, t]
%Y A359382 Cf. A007947, A010846, A013929, A020639, A024619, A027750, A126706, A162306, A243822, A272618, A355432, A359929, A360589, A360768.
%K A359382 nonn
%O A359382 1,4
%A A359382 _Michael De Vlieger_, Mar 29 2023