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

1,2

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.

Links

Table of n, a(n) for n=1..36.

Formula

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

a(n) >= A038547(n).

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]

Crossrefs

Cf. A038547, A326835, A328858, A348198.

Sequence in context: A050869 A323679 A038547 * A242438 A355716 A083556

Adjacent sequences: A348196 A348197 A348198 * A348200 A348201 A348202

Keyword

nonn

Author

Amiram Eldar, Oct 06 2021

Status

approved