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

Author

Amiram Eldar, Mar 28 2018

Keywords

• nonn
• more

Comments

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

Examples

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

Crossrefs

Cf. A064379, A064380.

Programs

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 *)

Extensions

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

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