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A339821 a(n) = phi(A019565(2n)), where phi is Euler totient function.

%I A339821 #10 Dec 19 2020 08:00:16
%S A339821 1,2,4,8,6,12,24,48,10,20,40,80,60,120,240,480,12,24,48,96,72,144,288,
%T A339821 576,120,240,480,960,720,1440,2880,5760,16,32,64,128,96,192,384,768,
%U A339821 160,320,640,1280,960,1920,3840,7680,192,384,768,1536,1152,2304,4608,9216,1920,3840,7680,15360,11520,23040,46080,92160
%N A339821 a(n) = phi(A019565(2n)), where phi is Euler totient function.
%F A339821 If 4n = 2^e1 + 2^e2 + ... + 2^ek [e1 ... ek distinct], then a(n) = A006093(e1) * A006093(e2) * ... * A006093(ek).
%F A339821 a(n) = A339820(2n) = A000010(A019565(2n)) = A000010(A019565(2n+1)).
%F A339821 a(n) = A003972(A019565(n)) = A000010(A003961(A019565(n))).
%o A339821 (PARI)
%o A339821 A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); };
%o A339821 A339821(n) = eulerphi(A019565(n+n));
%o A339821 (PARI) A339821(n) = { my(m=1, p=2); while(n>0, p = nextprime(1+p); if(n%2, m *= (p-1)); n >>= 1); (m); };
%Y A339821 Bisection of A339820.
%Y A339821 Cf. A000010, A003961, A003972, A006093, A019565, A339822 (2-adic valuation).
%Y A339821 Cf. also A324651.
%K A339821 nonn
%O A339821 0,2
%A A339821 _Antti Karttunen_, Dec 18 2020