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A348199
a(n) is the least term of A326835 whose number of divisors is n.
1
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.
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
KEYWORD
nonn
AUTHOR
Amiram Eldar, Oct 06 2021
STATUS
approved