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A091495
Odd squarefree numbers k such that k/phi(k) > 2, where phi is Euler's totient function.
3
105, 165, 195, 1155, 1365, 1785, 1995, 2145, 2415, 2805, 3003, 3045, 3135, 3255, 3315, 3705, 3795, 3885, 3927, 4305, 4389, 4485, 4515, 4641, 4785, 4845, 4935, 5115, 5187, 5313, 5565, 5655, 5865, 6045, 6105, 6195, 6405, 6555, 6765, 7035, 7095, 7215
OFFSET
1,1
COMMENTS
Apparently the squarefree members of the sequence A036798. Note that 105, 165 and 195 are the only terms having 3 prime factors. Also note that all the numbers listed above have 3 as a factor. The smallest number of this form not divisible by 3 is 37182145 = 5*7*11*13*17*19*23.
From Amiram Eldar, Nov 21 2024: (Start)
If k is term and m is an odd squarefree number coprime to k, then k*m is also a term.
The numbers of terms that do not exceed 10^k, for k = 3, 4, ..., are 3, 58, 513, 5108, 52365, 523975, 5214831, 52103339, 521507571, ... . Apparently, the asymptotic density of this sequence exists and equals 0.00521... . (End)
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)
MATHEMATICA
lst={}; Do[f=FactorInteger[n]; s=Times@@Last/@f; If[s==1&&Times@@(1-1/(First/@f))<1/2, AppendTo[lst, n]], {n, 3, 10000, 2}]; lst
Select[Range[1, 7301, 2], SquareFreeQ[#]&&#/EulerPhi[#]>2&] (* Harvey P. Dale, Jul 10 2017 *)
PROG
(PARI) is(k) = if(!(k%2), 0, my(f=factor(k)); issquarefree(f) && k / eulerphi(f) > 2); \\ Amiram Eldar, Nov 21 2024
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
T. D. Noe, Jan 15 2004
STATUS
approved