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A376212 a(n) is the least k such that A001615(k) = 2*n, or -1 if there is no such k, where A001615 is the Dedekind psi function.

%I A376212 #11 Sep 20 2024 05:51:51
%S A376212 -1,3,4,7,-1,6,13,-1,10,19,-1,12,-1,-1,25,21,-1,18,37,-1,26,43,-1,24,
%T A376212 -1,-1,34,39,-1,38,61,-1,-1,67,-1,30,73,-1,-1,57,-1,52,-1,-1,50,-1,-1,
%U A376212 42,97,-1,101,103,-1,54,109,91,74,-1,-1,75,-1,-1,82,93,-1,86,-1,-1,137,139,-1,60,-1,-1
%N A376212 a(n) is the least k such that A001615(k) = 2*n, or -1 if there is no such k, where A001615 is the Dedekind psi function.
%C A376212 Since A001615(k) > k for k > 1, a(n) < 2*n.
%H A376212 Robert Israel, <a href="/A376212/b376212.txt">Table of n, a(n) for n = 1..10000</a>
%e A376212 a(3) = 4 because A001615(4) = 6.
%p A376212 psi:= proc(n) local p;
%p A376212    n * mul(1+1/p, p = numtheory:-factorset(n))
%p A376212 end proc:
%p A376212 N:= 100: # for a(1) to a(N)
%p A376212 V:= Vector(N,-1):
%p A376212 for k from 3 to 2*N-1 do
%p A376212  v:= psi(k)/2;
%p A376212    if v <= N and V[v] = -1 then V[v]:= k fi
%p A376212 od:
%p A376212 convert(V,list);
%Y A376212 Cf. A001615, A203444, A291487.
%K A376212 sign,look
%O A376212 1,2
%A A376212 _Robert Israel_, Sep 15 2024