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A147516
List giving least odd integer of each prime signature.
10
1, 3, 9, 15, 27, 45, 81, 105, 135, 225, 243, 315, 405, 675, 729, 945, 1155, 1215, 1575, 2025, 2187, 2835, 3375, 3465, 3645, 4725, 6075, 6561, 8505, 10125, 10395, 10935, 11025, 14175, 15015, 17325, 18225, 19683, 23625, 25515, 30375, 31185, 32805
OFFSET
1,2
COMMENTS
All numbers of the form 3^k2*5^k3*...*p_n^k_n, where k2 >= k3 >= ... >= k_n, sorted.
LINKS
David Ryan, Mathematical Harmony Analysis, arXiv preprint arXiv:1603.08904 [cs.SD], 2016-2017.
FORMULA
Sum_{n>=1} 1/a(n) = Product_{n>=2} 1/(1 - 1/A070826(n)) = 1.6241170949... - Amiram Eldar, Oct 20 2020
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
Sequence in context: A082897 A363523 A339886 * A372509 A233819 A131822
KEYWORD
nonn
AUTHOR
Will Nicholes, Nov 05 2008
EXTENSIONS
Edited and extended by Ray Chandler, Jul 29 2010
STATUS
approved