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 A327171 a(n) = phi(n) * core(n), where phi is Euler totient function, and core gives the squarefree part of n. 3
 1, 2, 6, 2, 20, 12, 42, 8, 6, 40, 110, 12, 156, 84, 120, 8, 272, 12, 342, 40, 252, 220, 506, 48, 20, 312, 54, 84, 812, 240, 930, 32, 660, 544, 840, 12, 1332, 684, 936, 160, 1640, 504, 1806, 220, 120, 1012, 2162, 48, 42, 40, 1632, 312, 2756, 108, 2200, 336, 2052, 1624, 3422, 240, 3660, 1860, 252, 32, 3120, 1320 (list; graph; refs; listen; history; text; internal format)
 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 a(n) = A000010(n) * A007913(n). 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 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 CROSSREFS Cf. A082473 (gives the terms in ascending order, with duplicates removed). Cf. A000010, A007913, A327170, A327172, A248003. Cf. also A002618, A062355. Sequence in context: A174857 A248568 A257252 * A008556 A254638 A320118 Adjacent sequences:  A327168 A327169 A327170 * A327172 A327173 A327174 KEYWORD nonn,mult AUTHOR Antti Karttunen, Sep 28 2019 STATUS approved

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Last modified May 7 16:00 EDT 2021. Contains 343652 sequences. (Running on oeis4.)