OFFSET
1,2
REFERENCES
Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 161.
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..20000
Chantal David and Francesco Pappalardi, Average Frobenius distributions of elliptic curves, International Mathematics Research Notices, Vol. 1999, No. 4 (1999), pp. 165-183, alternative link.
FORMULA
Multiplicative with a(p^k) = (p-1) * p^((k-1)+(k mod 2)).
Sum_{n>=1} 1/a(n) = (Pi^2/6) * Product_{p prime} (1 + (p+1)/(p^2*(p-1))) = 3.96555686901754604330... - Amiram Eldar, Oct 16 2020
Sum_{k=1..n} a(k) ~ c * n^3, where c = (Pi^2/45) * Product_{p prime} (1 - 1/p^2 + 1/p^3 - 1/p^4) = 0.1500809164... . - Amiram Eldar, Dec 05 2022
MATHEMATICA
Array[EulerPhi[#] (Sqrt@ # /. (c_: 1) a_^(b_: 0) :> (c a^b)^2) &, 66] (* Michael De Vlieger, Sep 29 2019, after Bill Gosper at A007913 *)
PROG
(PARI) A327171(n) = eulerphi(n)*core(n);
(PARI) A327171(n) = { my(f=factor(n)); prod (i=1, #f~, (f[i, 1]-1)*(f[i, 1]^(-1 + f[i, 2] + (f[i, 2]%2)))); };
(Python)
from sympy.ntheory.factor_ import totient, core
def A327171(n):
return totient(n)*core(n) # Chai Wah Wu, Sep 29 2019
(Magma) [EulerPhi(n)*Squarefree(n): n in [1..100]]; // G. C. Greubel, Jul 13 2024
(SageMath) [euler_phi(n)*squarefree_part(n) for n in range(1, 101)] # G. C. Greubel, Jul 13 2024
CROSSREFS
Cf. A082473 (gives the terms in ascending order, with duplicates removed).
KEYWORD
nonn,easy,mult
AUTHOR
Antti Karttunen, Sep 28 2019
STATUS
approved