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%I #9 Apr 01 2023 22:05:44
%S 1,3,4,5,-1,7,8,9,-1,11,-1,13,-1,24,16,17,-1,19,-1,33,-1,23,-1,25,-1,
%T 27,-1,29,-1,31,32,45,-1,-1,-1,37,-1,-1,-1,41,-1,43,-1,69,-1,47,-1,49,
%U -1,-1,-1,53,-1,76,-1,72,-1,59,-1,61,-1,96,64,85,-1,67,-1,-1,-1,71,-1,73,-1,-1,-1,-1,-1,79,-1,81,-1,83,-1,104,-1,-1,-1
%N An inverse of the unitary totient function A047994.
%C a(n) is the smallest m such that A047994(m)=n, or -1 if this m does not exist. Proof of nonexistence may be done by transversing all A045778(n) factorizations of n, increasing each factor in these factorizations by 1 and showing that none of these modified products is a product of powers of distinct primes.
%H Amiram Eldar, <a href="/A135347/b135347.txt">Table of n, a(n) for n = 1..10000</a>
%t a[n_] := Module[{v = invUPhi[n]}, If[v == {}, -1, v[[1]]]]; Array[a, 100] (* _Amiram Eldar_, Apr 01 2023, using the function invUPhi from A361966 *)
%Y Cf. A047994, A045778, A361966.
%K sign
%O 1,2
%A _R. J. Mathar_, Dec 07 2007
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