A301866 Numbers k such that iphi(k) = iphi(k+1), where iphi is the infinitary totient function (A064380).

1, 21, 143, 208, 314, 459, 957, 1652, 2685, 5091, 20155, 38180, 41265, 45716, 54722, 116937, 161001, 186794, 230390, 274533, 338547, 416577, 430137, 495187

Offset

1,2

Comments

a(16) > 10^5. - Robert Price, May 22 2018

Links

Table of n, a(n) for n=1..24.

Example

iphi(21) = iphi(22) = 14, thus 21 is in the sequence.

Mathematica

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]]]]]];
  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 *)

Crossrefs

Cf. A064379, A064380.

Sequence in context: A107731 A003702 A221785 * A377166 A101645 A391711

Adjacent sequences: A301863 A301864 A301865 * A301867 A301868 A301869

Keyword

nonn,more

Author

Amiram Eldar, Mar 28 2018

Extensions

a(11)-a(15) from Robert Price, May 22 2018

a(16)-a(24) from Amiram Eldar, Mar 26 2023

Status

approved