A349428 Smallest k such that A349410(k) = n or -1 if no such number exists.
1, 4, 15, 30, 42, 360, 196, 525, 2080, 320, 7168, 123200, 35200, 150920, 196000, 1232000, 61236, 466560, 106831872, 49787136, 14580000, 155648000, 94058496, 123561984, 47385000
Offset: 1
Programs
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Mathematica
f[n_] := Module[{s = NestWhileList[n * DivisorSigma[0, #] &, 1, UnsameQ, All]}, Differences[Position[s, s[[-1]]]][[1, 1]]]; seq[len_, nmax_] := Module[{v = Table[0, {len}], n = 1, c = 0, i}, While[c < len && n < nmax, i = f[n]; If[i <= len && v[[i]] == 0, c++; v[[i]] = n]; n++]; TakeWhile[v, # > 0 &]]; seq[15, 10^6] (* Amiram Eldar, Nov 17 2021 *)
Extensions
Escape clause value changed to -1. - N. J. A. Sloane, Jan 14 2022