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URL: https://oeis.org/A385747

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A385747
Least number that reaches 1 after exactly n iterations of the infinitary analog of the totient function A384247.
3
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
0,2
COMMENTS
a(n) is the least number k such that A385744(k) = n.
Also, indices of records of A385744.
EXAMPLE
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
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]
PROG
(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++)); }
CROSSREFS
Similar sequences: A003271, A005424, A007755, A333610.
Sequence in context: A068584 A107799 A329049 * A003271 A049796 A106165
KEYWORD
nonn
AUTHOR
Amiram Eldar, Jul 08 2025
STATUS
approved