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

1, 2, 4, 8, 6, 12, 24, 48, 10, 20, 40, 80, 60, 120, 240, 480, 12, 24, 48, 96, 72, 144, 288, 576, 120, 240, 480, 960, 720, 1440, 2880, 5760, 16, 32, 64, 128, 96, 192, 384, 768, 160, 320, 640, 1280, 960, 1920, 3840, 7680, 192, 384, 768, 1536, 1152, 2304, 4608, 9216, 1920, 3840, 7680, 15360, 11520, 23040, 46080, 92160

Offset: 0

Author

Antti Karttunen, Dec 18 2020

Keywords

• nonn

Crossrefs

Bisection of A339820.

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

Cf. also A324651.

Programs

PARI

A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); };
A339821(n) = eulerphi(A019565(n+n));

PARI

A339821(n) = { my(m=1, p=2); while(n>0, p = nextprime(1+p); if(n%2, m *= (p-1)); n >>= 1); (m); };

Formula

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

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

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