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A382408 a(n) is the number of terms in A071174 whose radical is A144338(n).

%I A382408 #11 Apr 26 2025 03:33:06
%S A382408 1,1,1,5,1,9,1,1,13,14,1,1,20,21,1,25,1,406,1,32,33,34,1,37,38,1,820,
%T A382408 1,45,1,50,1,54,56,57,1,1,61,64,2080,1,68,2346,1,1,73,76,2926,1,81,1,
%U A382408 84,85,86,1,90,92,93,94,1,1,5050,1,5356,105,1,1,5886,110
%N A382408 a(n) is the number of terms in A071174 whose radical is A144338(n).
%C A382408 a(n) is the number of positive integers k for which A007947(A071174(k)) = A144338(n).
%H A382408 Felix Huber, <a href="/A382408/b382408.txt">Table of n, a(n) for n = 1..10000</a>
%F A382408 a(n) = binomial(A144338(n) - 1, A144338(n) - Omega(A144338(n))).
%e A382408 The a(6) = 9 numbers in A071174 that have the radical A144338(6) = 10 are 2^9*5^1 = 2560, 2^8*5^2 = 6400, 2^7*5^3 = 16000, 2^6*5^4 = 40000, 2^5*5^5 = 100000, 2^4*5^6 = 250000, 2^3*5^7 = 625000, 2^2*5^8 = 1562500, 2^1*5^9 = 3906250.
%p A382408 A144338:=proc(n)
%p A382408     option remember;
%p A382408     local a;
%p A382408     if n=1 then
%p A382408         2
%p A382408     else
%p A382408         for a from procname(n-1)+1 do
%p A382408             if IsSquareFree(a) then
%p A382408                 return a
%p A382408             fi
%p A382408         od
%p A382408     fi;
%p A382408 end proc;
%p A382408 A382408:=n->binomial(A144338(n)-1,A144338(n)-NumberTheory:-Omega(A144338(n)));
%p A382408 seq(A382408(n),n=1..69);
%Y A382408 Cf. A007947, A071174, A144338.
%K A382408 nonn
%O A382408 1,4
%A A382408 _Felix Huber_, Apr 04 2025