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A307055 Even k such that psi(m) = k has no solution, where psi is the Dedekind psi function A001615.

%I A307055 #32 Aug 01 2020 10:49:53
%S A307055 2,10,16,22,26,28,34,40,46,50,52,58,64,66,70,76,78,82,86,88,92,94,100,
%T A307055 106,116,118,122,124,130,134,136,142,146,148,154,156,166,170,172,178,
%U A307055 184,188,190,196,202,206,208,210,214,218,220,226,232,236,238,244,246,250
%N A307055 Even k such that psi(m) = k has no solution, where psi is the Dedekind psi function A001615.
%C A307055 Analog of the nontotients A005277.
%C A307055 Contains 2*p if p is in A307390. - _Robert Israel_, Apr 17 2019
%H A307055 Robert Israel, <a href="/A307055/b307055.txt">Table of n, a(n) for n = 1..10000</a>
%e A307055 2 is a term because there exists no m such that psi(m) = 2.
%e A307055 4 is not a term because 4 = 3*(3+1)/3.
%p A307055 N:= 1000: # to get all terms <= N
%p A307055 psi:= proc(n) local p; n*mul(1+1/p, p=numtheory:-factorset(n)) end proc:
%p A307055 sort(convert({seq(i,i=2..N,2)} minus map(psi, {$1..N}), list)); # _Robert Israel_, Apr 17 2019
%t A307055 M = 1000; (* to get all terms <= M *)
%t A307055 psi[n_] := n Sum[MoebiusMu[d]^2/d, {d, Divisors[n]}];
%t A307055 Range[2, M, 2] ~Complement~ (psi /@ Range[M]) (* _Jean-François Alcover_, Aug 01 2020, after Maple *)
%o A307055 (PARI) dpsi(n) = = n * sumdivmult(n, d, issquarefree(d)/d); \\ A001615
%o A307055 isok(n) = {if (!(n%2), for (k=1, n-1,  if (dpsi(k) == n, return(0));); return (1););} \\ _Michel Marcus_, Mar 22 2019
%Y A307055 Cf. A001615, A005277, A005382.
%K A307055 nonn
%O A307055 1,1
%A A307055 _Torlach Rush_, Mar 21 2019