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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.

%I A382964 #34 May 09 2025 00:56:44
%S A382964 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,
%T A382964 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,
%U A382964 7,4,13,1,7,1,7,4,7,3,18,1,7,1,7,1,19,3
%N 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.
%H A382964 Michael De Vlieger, <a href="/A382964/b382964.txt">Table of n, a(n) for n = 1..10000</a>
%F A382964 a(n) = 1 for n in A246655.
%F A382964 1+A001221(n) <= a(n) < A010846(n) for n in A024619.
%e A382964 Table of select n, a(n), and numbers k in row n of A382926:
%e A382964  n  a(n)    row n of A382926
%e A382964 --------------------------------------------------------
%e A382964  6    3     3, 4, 6;
%e A382964 10    4     4, 5, 8, 10;
%e A382964 12    4     6, 8, 9, 12;
%e A382964 14    4     4, 7, 8, 14;
%e A382964 15    3     5, 9, 15;
%e A382964 18    5     8, 9, 12, 16, 18;
%e A382964 20    5     5, 8, 10, 16, 20;
%e A382964 21    3     7, 9, 21;
%e A382964 22    5     4, 8, 11, 16, 22;
%e A382964 24    5     9, 12, 16, 18, 24;
%e A382964 26    5     4, 8, 13, 16, 26;
%e A382964 28    5     7, 8, 14, 16, 28;
%e A382964 30   12     8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30.
%t A382964 (* First, run the "regs" function from A369609, then: *)
%t A382964 Table[Count[regs[n], _?(Function[k, AllTrue[FactorInteger[n][[All, 1]], #*k > n &]])], {n, 105}]
%Y A382964 Cf. A007947, A010846, A024619, A162306, A246655, A382926.
%K A382964 nonn
%O A382964 1,6
%A A382964 _Michael De Vlieger_, Apr 28 2025