A362025 a(n) is the least number that reaches 1 after n iterations of the infinitary totient function A064380.

2, 3, 4, 5, 9, 11, 16, 17, 28, 29, 46, 47, 99, 145, 167, 205, 314, 397, 437, 793, 851, 1137, 1693, 2453, 2771, 2989, 3701, 5099, 6801, 9299, 12031, 15811, 16816, 21520, 21521, 29547, 39685, 62077, 83191, 103473, 112117, 149535, 157159, 196049, 200267, 303022

Offset

1,1

Links

Table of n, a(n) for n=1..46.

Formula

A362024(a(n)) = n, and A362024(k) < n for all k < a(n).

Mathematica

infCoprimeQ[n1_, n2_] := Module[{g = GCD[n1, n2]}, If[g == 1, True, AllTrue[FactorInteger[g][[;; , 1]], BitAnd @@ IntegerExponent[{n1, n2}, #] == 0 &]]];
iphi[n_] := Sum[Boole[infCoprimeQ[j, n]], {j, 1, n - 1}];
numiter[n_] := Length@ NestWhileList[iphi, n, # > 1 &] - 1;
seq[kmax_] := Module[{v = {}, n = 1}, Do[If[numiter[k] == n, AppendTo[v, k]; n++], {k, 2, kmax}]; v]; seq[1000]

Prog

(PARI) isinfcoprime(n1, n2) = {my(g = gcd(n1, n2), p, e1, e2); if(g == 1, return(1)); p = factor(g)[, 1]; for(i=1, #p, e1 = valuation(n1, p[i]); e2 = valuation(n2, p[i]); if(bitand(e1, e2) > 0, return(0))); 1; }
iphi(n) = sum(j = 1, n-1, isinfcoprime(j, n));
numiter(n) = if(n==2, 1, numiter(iphi(n)) + 1);
lista(kmax) = {my(n = 1); for(k = 2, kmax, if(numiter(k) == n, print1(k, ", "); n++)); }

Crossrefs

Cf. A064380.

Indices of records of A362024.

Similar sequences: A003271, A007755, A333610.

Sequence in context: A100797 A139441 A333612 * A093305 A065817 A361227

Adjacent sequences: A362022 A362023 A362024 * A362026 A362027 A362028

Keyword

nonn

Author

Amiram Eldar, Apr 05 2023

Status

approved