A147516 List giving least odd integer of each prime signature.

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

Author

Will Nicholes, Nov 05 2008

Keywords

• nonn

Comments

All numbers of the form 3^k2*5^k3*...*p_n^k_n, where k2 >= k3 >= ... >= k_n, sorted.

Links

• Ray Chandler, Table of n, a(n) for n = 1..10000
• David Ryan, Mathematical Harmony Analysis, arXiv preprint arXiv:1603.08904 [cs.SD], 2016-2017.

Crossrefs

Multiplicative closure of A001147.

Cf. A025487, A070826.

Programs

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 *)

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

Formula

Sum_{n>=1} 1/a(n) = Product_{n>=2} 1/(1 - 1/A070826(n)) = 1.6241170949... - Amiram Eldar, Oct 20 2020

Extensions

Edited and extended by Ray Chandler, Jul 29 2010