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A122254
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Numbers with 3-smooth Euler's totient (A000010).
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8
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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
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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FORMULA
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Sum_{n>=1} 1/a(n) = 3 * Product_{p > 3 in A005109} (1 + 1/p) = 5.38288865867495675807... . - Amiram Eldar, Dec 03 2022
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MATHEMATICA
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Select[Range@115, Max[FactorInteger[EulerPhi[#]][[All, 1]]] < 5 &] (* Ivan Neretin, Jul 28 2015 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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