login
A122254
Numbers with 3-smooth Euler's totient (A000010).
8
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 24, 26, 27, 28, 30, 32, 34, 35, 36, 37, 38, 39, 40, 42, 45, 48, 51, 52, 54, 56, 57, 60, 63, 64, 65, 68, 70, 72, 73, 74, 76, 78, 80, 81, 84, 85, 90, 91, 95, 96, 97, 102, 104, 105, 108, 109, 111, 112, 114
OFFSET
1,2
COMMENTS
An integer n>=3 belongs to this sequence if and only if a regular n-gon can be constructed using straightedge and conic sections (details in Gibbins and Smolinsky, see below). - Austin Shapiro, Nov 14 2021
Products of 3-smooth numbers (A003586) and squarefree numbers whose prime factors are all Pierpont primes (A005109). - Amiram Eldar, Dec 03 2022
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Aliska Gibbins and Lawrence Smolinsky, Geometric Constructions with Ellipses, The Mathematical Intelligencer 31(1) (2009), 57-62.
FORMULA
a(n) = A048135(n-2) for n>2.
a(n) = A122260(n) = A048737(n) for n < 22.
Sum_{n>=1} 1/a(n) = 3 * Product_{p > 3 in A005109} (1 + 1/p) = 5.38288865867495675807... . - Amiram Eldar, Dec 03 2022
MATHEMATICA
Select[Range@115, Max[FactorInteger[EulerPhi[#]][[All, 1]]] < 5 &] (* Ivan Neretin, Jul 28 2015 *)
PROG
(PARI) is(n)=n=eulerphi(n); n>>=valuation(n, 2); n==3^valuation(n, 3) \\ Charles R Greathouse IV, Feb 21 2013
(PARI) list(lim)=my(v=List(), u, t); for(i=0, log(lim--+1.5)\log(3), t=3^i; while(t<=lim, if(isprime(t+1), listput(v, t+1)); t<<=1)); v=vecsort(Vec(v)); u=List([1]); for(i=3, #v, for(j=1, #u, t=v[i]*u[j]; if(t>lim, next(2)); listput(u, t))); u=vecsort(Vec(u)); v=List(u); for(i=1, #u, t=u[i]; while((t*=3)<=lim, listput(v, t))); u=Vec(v); v=List(u); for(i=1, #u, t=u[i]; while((t<<=1)<=lim, listput(v, t))); vecsort(Vec(v)) \\ Charles R Greathouse IV, Feb 22 2013
CROSSREFS
Cf. A000010, A003586 (3-smooth), A005109.
Subsequence of A122260.
Sequence in context: A023752 A048737 A122260 * A249626 A102823 A179308
KEYWORD
nonn,easy
AUTHOR
Reinhard Zumkeller, Aug 29 2006
STATUS
approved