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%I #33 Jun 19 2021 03:31:23
%S 1,3,9,15,27,45,81,105,135,225,243,315,405,675,729,945,1155,1215,1575,
%T 2025,2187,2835,3375,3465,3645,4725,6075,6561,8505,10125,10395,10935,
%U 11025,14175,15015,17325,18225,19683,23625,25515,30375,31185,32805
%N List giving least odd integer of each prime signature.
%C All numbers of the form 3^k2*5^k3*...*p_n^k_n, where k2 >= k3 >= ... >= k_n, sorted.
%H Ray Chandler, <a href="/A147516/b147516.txt">Table of n, a(n) for n = 1..10000</a>
%H David Ryan, <a href="https://arxiv.org/abs/1603.08904">Mathematical Harmony Analysis</a>, arXiv preprint arXiv:1603.08904 [cs.SD], 2016-2017.
%F Sum_{n>=1} 1/a(n) = Product_{n>=2} 1/(1 - 1/A070826(n)) = 1.6241170949... - _Amiram Eldar_, Oct 20 2020
%t PrimeExponents[n_] := FactorInteger[n][[All, 2]]; lpe = {}; A147516 = {1}; Do[pe = PrimeExponents[n] // Sort; If[FreeQ[lpe, pe], AppendTo[lpe, pe]; AppendTo[A147516, n]], {n, 3, 40000, 2}]; A147516 (* _Jean-François Alcover_, Jan 27 2015, after _Robert G. Wilson v_ *)
%o (PARI) is(n)=my(k=oo, t); forprime(p=3,, t=valuation(n, p); if(t>k, return(0), k=t); if(k, n/=p^k, return(n==1))) \\ _Charles R Greathouse IV_, Aug 20 2015
%Y Cf. A025487, A070826.
%K nonn
%O 1,2
%A _Will Nicholes_, Nov 05 2008
%E Edited and extended by _Ray Chandler_, Jul 29 2010
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