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A122819 Array read by rows in which the n-th row contains smallest odd numbers in increasing order of all possible prime signatures with n divisors.

%I A122819 #10 Jun 29 2025 03:24:25
%S A122819 1,3,9,15,27,81,45,243,729,105,135,2187,225,6561,405,19683,59049,315,
%T A122819 675,1215,177147,531441,3645,1594323,2025,4782969,945,1155,3375,10935,
%U A122819 14348907,43046721,1575,6075,32805,129140163,387420489,2835,10125,98415
%N A122819 Array read by rows in which the n-th row contains smallest odd numbers in increasing order of all possible prime signatures with n divisors.
%C A122819 n-th row contains A001055(n) terms.
%C A122819 First item of each row gives A038547.
%H A122819 Amiram Eldar, <a href="/A122819/b122819.txt">Table of n, a(n) for n = 1..7314</a> (rows n=1..1000, flattened)
%e A122819 Table begins:
%e A122819   1,
%e A122819   3,
%e A122819   9,
%e A122819   15, 27,
%e A122819   81,
%e A122819   45, 243,
%e A122819   729,
%e A122819   105, 135, 2187,
%e A122819   ...
%t A122819 row[n_] := Module[{e = f[n] - 1}, Sort[Times @@ (Prime[Range[2, Length[#]+1]]^Reverse[#]) & /@ e]]; Table[row[n], {n, 1, 25}] // Flatten (* _Amiram Eldar_, Jun 28 2025 using the function f by _T. D. Noe_ at A162247 *)
%Y A122819 Cf. A001055, A038547, A077569, A162247.
%K A122819 nonn,tabf
%O A122819 1,2
%A A122819 _Ray Chandler_, Sep 22 2006