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a(n) is the least number k such that A348264(k) = n, or -1 if no such number exists.
0

%I #4 Oct 09 2021 07:19:13

%S 1,2,84,1596,410652,9114300,10628100,3012406320

%N a(n) is the least number k such that A348264(k) = n, or -1 if no such number exists.

%e n The n iterations of a(n) under the map x -> A348264(x)

%e - --------------------------------------------------------------------------------

%e 0 1

%e 1 2 -> 1

%e 2 84 -> 78 -> 39

%e 3 1596 -> 1428 -> 1326 -> 663

%e 4 410652 -> 410172 -> 366996 -> 340782 -> 170391

%e 5 9114300 -> 8871252 -> 8680848 -> 8661648 -> 8487018 -> 4243509

%e 6 10628100 -> 10344684 -> 10309980 -> 10287900 -> 10013556 -> 9298302 -> 4649151

%e 7 3012406320 -> 2999958360 -> 2927545572 -> 2917724340 -> 2911475700 -> 2833836348 -> 2631419466 -> 1315709733

%t f[p_, e_] := p^e - 1; uphi[1] = 1; uphi[n_] := Times @@ f @@@ FactorInteger[n]; sum[n_] := Plus @@ DeleteDuplicates[uphi /@ Select[Divisors[n], CoprimeQ[#, n/#] &]]; s[n_] := -2 + Length@FixedPointList[sum, n]; seq[m_, lim_] := Module[{t = Table[0, {m}], c = 0, n = 1}, While[c < m && n < lim, i = s[n] + 1; If[i <= m && t[[i]] == 0, c++; t[[i]] = n]; n++]; TakeWhile[t, # > 0 &]]; seq[5, 10^6]

%Y The unitary version of A348214.

%Y Cf. A348004, A348264.

%K nonn,more

%O 0,2

%A _Amiram Eldar_, Oct 09 2021