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A333909
Numbers k such that phi(k) is the sum of 2 squares, where phi is the Euler totient function (A000010).
4
1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 16, 17, 19, 20, 22, 24, 25, 27, 30, 32, 33, 34, 37, 38, 40, 41, 44, 48, 50, 51, 53, 54, 55, 57, 59, 60, 63, 64, 66, 68, 73, 74, 75, 76, 80, 82, 83, 85, 88, 91, 95, 96, 100, 101, 102, 106, 107, 108, 110, 111, 114, 117, 118, 120
OFFSET
1,2
LINKS
William D. Banks, Florian Luca, Filip Saidak, and Igor E. Shparlinski, Values of arithmetical functions equal to a sum of two squares, Quarterly Journal of Mathematics, Vol. 56, No. 2 (2005), pp. 123-139, alternative link.
FORMULA
c1 * x/log(x)^(3/2) < N(x) < c2 * x/log(x)^(3/2), where N(x) is the number of terms <= x, and c1 and c2 are two positive constants (Banks et al., 2005).
EXAMPLE
1 is a term since phi(1) = 1 = 0^2 + 1^2.
MATHEMATICA
Select[Range[120], SquaresR[2, EulerPhi[#]] > 0 &]
PROG
(Python)
from itertools import count, islice
from sympy import factorint, totient
def A333909_gen(): # generator of terms
return filter(lambda n:all(p & 3 != 3 or e & 1 == 0 for p, e in factorint(totient(n)).items()), count(1))
A333909_list = list(islice(A333909_gen(), 30)) # Chai Wah Wu, Jun 27 2022
KEYWORD
nonn
AUTHOR
Amiram Eldar, Apr 09 2020
STATUS
approved