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

%I A362025 #6 Apr 07 2023 17:42:13
%S A362025 2,3,4,5,9,11,16,17,28,29,46,47,99,145,167,205,314,397,437,793,851,
%T A362025 1137,1693,2453,2771,2989,3701,5099,6801,9299,12031,15811,16816,21520,
%U A362025 21521,29547,39685,62077,83191,103473,112117,149535,157159,196049,200267,303022
%N A362025 a(n) is the least number that reaches 1 after n iterations of the infinitary totient function A064380.
%F A362025 A362024(a(n)) = n, and A362024(k) < n for all k < a(n).
%t A362025 infCoprimeQ[n1_, n2_] := Module[{g = GCD[n1, n2]}, If[g == 1, True, AllTrue[FactorInteger[g][[;; , 1]], BitAnd @@ IntegerExponent[{n1, n2}, #] == 0 &]]];
%t A362025 iphi[n_] := Sum[Boole[infCoprimeQ[j, n]], {j, 1, n - 1}];
%t A362025 numiter[n_] := Length@ NestWhileList[iphi, n, # > 1 &] - 1;
%t A362025 seq[kmax_] := Module[{v = {}, n = 1}, Do[If[numiter[k] == n, AppendTo[v, k]; n++], {k, 2, kmax}]; v]; seq[1000]
%o A362025 (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; }
%o A362025 iphi(n) = sum(j = 1, n-1, isinfcoprime(j, n));
%o A362025 numiter(n) = if(n==2, 1, numiter(iphi(n)) + 1);
%o A362025 lista(kmax) = {my(n = 1); for(k = 2, kmax, if(numiter(k) == n, print1(k, ", "); n++)); }
%Y A362025 Cf. A064380.
%Y A362025 Indices of records of A362024.
%Y A362025 Similar sequences: A003271, A007755, A333610.
%K A362025 nonn
%O A362025 1,1
%A A362025 _Amiram Eldar_, Apr 05 2023