A300911 a(n) is the smallest positive integer k such that psi(x) = k has exactly n solutions, where psi(x) = A001615(x).

2, 1, 6, 84, 12, 24, 48, 168, 96, 72, 192, 144, 384, 672, 360, 960, 432, 288, 3648, 1080, 3600, 720, 2736, 1008, 576, 864, 11664, 6720, 7680, 1152, 7920, 6336, 2016, 1440, 3024, 1728, 2160, 14256, 5040, 2592, 2304, 13440, 9072, 10800, 43008, 26208, 24480, 4608, 2880, 10944, 6480

Offset: 0

Author

Altug Alkan, Mar 15 2018

Keywords

• nonn

Examples

			a(3) = 84 because psi(2^2*13) = psi(5*13) = psi(83) = 84 and 84 is the least number with this property.
		

Crossrefs

Cf. A001615, A007368, A007374.

Programs

Mathematica

psi[n_] := If[n == 1, 1, n Times @@ (1 + 1/First /@ FactorInteger@n)]; t = Sort[Reverse /@ Tally[Array[psi, 50000]]]; L = {2}; Do[ If[t[[j, 1]] == Length@ L, AppendTo[L, t[[j, 2]]]], {j, Length@t}]; L (* Giovanni Resta, Mar 16 2018 *)

PARI

{my(N=5*10^4, c=vectorsmall(N), i); A300911=List(); for(n=1,N,(i=A001615(n))>N||c[i]++); for(n=1,oo, for(i=1,N, c[i]==n && listput(A300911,i) && next(2)); break)} \\ M. F. Hasler, Mar 18 2018