%I #16 Mar 26 2023 02:20:06
%S 1,21,143,208,314,459,957,1652,2685,5091,20155,38180,41265,45716,
%T 54722,116937,161001,186794,230390,274533,338547,416577,430137,495187
%N Numbers k such that iphi(k) = iphi(k+1), where iphi is the infinitary totient function (A064380).
%C a(16) > 10^5. - _Robert Price_, May 22 2018
%e iphi(21) = iphi(22) = 14, thus 21 is in the sequence.
%t irelprime[n_] := Select[temp = iDivisors[n]; Range[n], Intersection[iDivisors[#], temp] === {1} &]; bitty[k_] := Union[Flatten[Outer[Plus, Sequence @@ {0, #1} & /@ Union[2^Range[0, Floor[Log[2, k]]]*Reverse[IntegerDigits[k, 2]]]]]];
%t iDivisors[k_Integer] := Sort[(Times @@ (First[it]^(#1 /. z -> List)) &) /@ Flatten[Outer[z, Sequence @@ bitty /@ Last[it = Transpose[FactorInteger[k]]], 1]]]; iDivisors[1] := {1}; iphi[n_] := Length[irelprime[n]]; iphiQ[n_] := iphi[n] == iphi[n + 1]; Select[Range[10^3], iphiQ](* after _Wouter Meeussen_ at A064379 *)
%Y Cf. A064379, A064380.
%K nonn,more
%O 1,2
%A _Amiram Eldar_, Mar 28 2018
%E a(11)-a(15) from _Robert Price_, May 22 2018
%E a(16)-a(24) from _Amiram Eldar_, Mar 26 2023