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%I #16 Apr 09 2023 02:48:37
%S 1,3,15,105,945,10395,135135,2297295,43648605,1003917915,25097947875,
%T 727840488375,22563055139625,834833040166125,34228154646811125,
%U 1471810649812878375,69175100541205283625,3389579926519058897625,179647736105510121574125,10599216430225097172873375,646552202243730927545275875
%N Smallest number with 2^n odd divisors.
%H Hartmut F. W. Hoft, <a href="/A360438/a360438.pdf">Computational Characterization of a(n) = A038547(2^n)</a>
%F a(n) = A038547(2^n).
%e a(4) = A038547(2^4) = 945 = 3^(2^2-1) * 5^(2^1-1) * 7^(2^1-1) = 3^3 * 5 * 7,
%e a(5) = A038547(2^5) = 10395 = 3^(2^2-1) * 5^(2^1-1) * 7^(2^1-1) * 11^(2^1-1) = 3^3 * 5 * 7 * 11,
%e a(24) = 3^3 * 5^3 * 7^3 * 11 * ... *79, and
%e a(25) = 3^7 * 5^3 * 7^3 * 11 * ... *79 since 79 < 3^4 < 83.
%t next[{num_, fList_, lastP_, {p_, k_}}] := Module[{nP, f1List, p1, k1}, nP=NextPrime[First[Last[fList]]]; If[nP<p^k, {num nP, Append[fList, {nP, 1}], nP, {p, k}}, f1List=Replace[fList, {p, k-1}->{p, 2k-1}, {1}]; {{p1, k1}}=FactorInteger[Min[Map[#[[1]]^(#[[2]]+1)&, f1List]]]; {num p^k, f1List, lastP, {p1, k1}}]]
%t a360438[n_] := Join[{1}, Map[First, NestList[next, {3, {{3, 1}}, 3, {3, 2}}, n-1]]]/;n>=1
%t Join[{1}, a360438[20]]
%Y Cf. A005179, A038547.
%K nonn
%O 0,2
%A _Hartmut F. W. Hoft_, Feb 07 2023
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