A385747 Least number that reaches 1 after exactly n iterations of the infinitary analog of the totient function A384247.

1, 2, 3, 4, 5, 9, 16, 17, 41, 73, 101, 197, 467, 829, 1109, 2761, 4849, 7831, 12401, 26189, 52379, 85853, 139589, 237007, 395533, 947043, 1967027, 3446033, 5396427, 9510437, 17502533, 35005067, 71202449, 90187609, 164664701, 395199461, 705113873, 1265735729, 1803553457

Offset: 0

Author

Amiram Eldar, Jul 08 2025

Keywords

• nonn

Comments

a(n) is the least number k such that A385744(k) = n.

Also, indices of records of A385744.

Examples

			  n | a(n) | iterations
  --+------+---------------------------
  1 |    2 | 2 -> 1
  2 |    3 | 3 -> 2 -> 1
  3 |    4 | 4 -> 3 -> 2 -> 1
  4 |    5 | 5 -> 4 -> 3 -> 2 -> 1
  5 |    9 | 9 -> 8 -> 4 -> 3 -> 2 -> 1
		

Crossrefs

Cf. A384247, A385744, A385745, A385746.

Similar sequences: A003271, A005424, A007755, A333610.

Programs

Mathematica

f[p_, e_] := p^e*(1 - 1/p^(2^(IntegerExponent[e, 2]))); iphi[1] = 1; iphi[n_] := iphi[n] = Times @@ f @@@ FactorInteger[n];
numiter[n_] := Length @ NestWhileList[iphi, n, # != 1 &] - 1;
seq[len_] := Module[{s = {}, k = 0, i = 0}, While[Length[s] < len, k++; If[numiter[k] == i, AppendTo[s, k]; i++]]; s]; seq[25]

PARI

iphi(n) = {my(f = factor(n)); n * prod(i = 1, #f~, (1 - 1/f[i, 1]^(1 << valuation(f[i, 2], 2))));}
numiter(n) = if(n ==  1, 0, 1 + numiter(iphi(n)));
list(len) = {my(k = 0, i = 0, c = 0); while(c < len, k++; if(numiter(k) == i, c++; print1(k, ", "); i++));}