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Numbers k such that all values of Euler phi (A000010) of all divisors of k are pairwise distinct and represent all proper divisors of k+1.
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%I #29 May 05 2024 01:28:52

%S 1,3,15,255,65535,4294967295

%N Numbers k such that all values of Euler phi (A000010) of all divisors of k are pairwise distinct and represent all proper divisors of k+1.

%C Numbers k such that {phi(d) : d|k} = {d : d|(k+1), d<(k+1)} as multisets.

%C Conjecture: last term is 4294967295.

%e 15 is in the sequence because {phi(d) : d|15} = {1, 2, 4, 8} = {d : d|16, d<16}.

%e 2 is not in the sequence because {phi(d) : d|2} = {1, 1}, but {d : d|2, d<2} = {1}.

%o (Magma) [n: n in [1..100000] | ([EulerPhi(d): d in Divisors(n)]) eq ([d: d in Divisors(n+1) | d lt n+1 ])]

%Y Subsequence of A250404 and A203966.

%Y Sequence differs from A051179, A050474 and A116518.

%Y Cf. A000010.

%K nonn,more,hard

%O 1,2

%A _Jaroslav Krizek_, Nov 22 2014

%E Edited and a(6) added by _Max Alekseyev_, May 04 2024