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

1,2

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.

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

Cf. A025487, A070826.

Sequence in context: A082897 A363523 A339886 * A372509 A233819 A131822

Adjacent sequences: A147513 A147514 A147515 * A147517 A147518 A147519

Keyword

nonn

Author

Will Nicholes, Nov 05 2008

Extensions

Edited and extended by Ray Chandler, Jul 29 2010

Status

approved