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%I #5 Oct 07 2021 02:15:52
%S 1,3,12,60,660,9240,157080,2984520,68643960,3226266120
%N Terms of A348004 having more unitary divisors than any smaller term.
%C The corresponding numbers of unitary divisors are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, ... (apparently, all the powers of 2).
%C a(11) > 7*10^10, if it exists.
%e The sequence A348004 begins with 1, 3, 4, 5, 7, 8, 9, 11 and 12. The number of unitary divisors of these terms are 1, 2, 2, 2, 2, 2, 2, 2 and 4, respectively. The record values, 1, 2 and 4, occur at 1, 3 and 12, the first 3 terms of this sequence.
%t f[p_, e_] := p^e - 1; uphi[1] = 1; uphi[n_] := Times @@ f @@@ FactorInteger[n]; q[n_] := Length @ Union[uphi /@ (d = Select[Divisors[n], CoprimeQ[#, n/#] &])] == Length[d]; dm = 0; s = {}; Do[If[q[n], d = 2^PrimeNu[n]; If[d > dm, dm = d; AppendTo[s, n]]], {n, 1, 10^6}]; s
%Y The unitary version of A348198.
%Y Cf. A348002, A348004.
%K nonn,more
%O 1,2
%A _Amiram Eldar_, Oct 06 2021