A339821 - OEIS

%I #10 Dec 19 2020 08:00:16

%S 1,2,4,8,6,12,24,48,10,20,40,80,60,120,240,480,12,24,48,96,72,144,288,

%T 576,120,240,480,960,720,1440,2880,5760,16,32,64,128,96,192,384,768,

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

%F If 4n = 2^e1 + 2^e2 + ... + 2^ek [e1 ... ek distinct], then a(n) = A006093(e1) * A006093(e2) * ... * A006093(ek).

%F a(n) = A339820(2n) = A000010(A019565(2n)) = A000010(A019565(2n+1)).

%F a(n) = A003972(A019565(n)) = A000010(A003961(A019565(n))).

%o (PARI)

%o A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); };

%o A339821(n) = eulerphi(A019565(n+n));

%o (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 Bisection of A339820.

%Y Cf. A000010, A003961, A003972, A006093, A019565, A339822 (2-adic valuation).

%Y Cf. also A324651.

%K nonn

%O 0,2

%A _Antti Karttunen_, Dec 18 2020