A348199 a(n) is the least term of A326835 whose number of divisors is n.

1, 3, 9, 15, 81, 45, 729, 105, 225, 405, 59049, 495, 531441, 3645, 2025, 1155, 43046721, 3675, 387420489, 4455, 18225, 295245, 31381059609, 8085, 50625, 2657205, 65025, 40095, 22876792454961, 34425, 205891132094649, 19635, 1476225, 215233605, 455625, 62475

Offset: 1

Author

Amiram Eldar, Oct 06 2021

Keywords

• nonn

Comments

First differs from A038547 at n = 12.

All the terms are odd since all the terms of A326835 are odd (as phi(1) = phi(2) = 1).

a(n) exists for any n since 3^(n-1) is a term of A326835 which has n divisors.

Crossrefs

Cf. A038547, A326835, A328858, A348198.

Programs

Mathematica

seq[m_] := Module[{p = Select[Range[m], PrimeQ], s = Table[0, {m}], c, nd, ndd}, s[[p]] = 3^(p - 1); c = Length[p]; n = 1; While[c < m, nd = DivisorSigma[0, n]; If[nd <= m && s[[nd]] == 0, ndd = Length@Union[EulerPhi /@ Divisors[n]]; If[ndd == nd, c++; s[[nd]] = n]]; n++]; s]; seq[30]

Formula

a(n) <= 3^(n-1), with equality if n is prime.

a(n) >= A038547(n).