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A341416 a(n) is the least k such that the product of indices of unitary prime power divisors of k is n.

%I A341416 #11 Feb 14 2021 02:50:59
%S A341416 1,3,4,5,7,8,9,11,13,16,17,19,23,25,27,29,31,32,37,35,36,47,49,40,59,
%T A341416 61,52,45,71,56,79,55,68,89,63,65,103,107,92,77,121,72,127,85,91,137,
%U A341416 139,88,151,112,124,115,169,104,119,99,148,193,197,133,211,223,117,145,161,136,241,155,196
%N A341416 a(n) is the least k such that the product of indices of unitary prime power divisors of k is n.
%C A341416 a(n) is the least k such that A333235(k) = n.
%C A341416 a(p) = A246655(p) for prime p.
%H A341416 Robert Israel, <a href="/A341416/b341416.txt">Table of n, a(n) for n = 1..10000</a>
%F A341416 A333235(a(n)) = n.
%e A341416 a(3) = 4 because A333235(4) = 3 and this is the first occurrence of 3 in A333235.
%p A341416 N:= 1000: # for a(1) to a(A025528(N))
%p A341416 R:= NULL: p:= 2:
%p A341416 while p < N do
%p A341416   R:= R,  seq(p^k,k=1..ilog[p](N));
%p A341416   p:= nextprime(p);
%p A341416 od:
%p A341416 L:= sort([R]):
%p A341416 M:= nops(L):
%p A341416 f:= proc(n) local F, t;
%p A341416   F:= ifactors(n)[2];
%p A341416   mul(ListTools:-BinarySearch(L,t[1]^t[2]),t=F)
%p A341416 end proc:
%p A341416 V:= Vector(M): count:= 0:
%p A341416 for n from 1 while count < M do
%p A341416   v:= f(n);
%p A341416 if v <= M and V[v] = 0 then count:= count+1; V[v]:= n fi;
%p A341416 od:
%p A341416 convert(V,list);
%Y A341416 Cf. A246655, A333235.
%K A341416 nonn,look
%O A341416 1,2
%A A341416 _Robert Israel_, Feb 11 2021