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

0,2

Links

Table of n, a(n) for n=0..63.

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))).

Prog

(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); };

Crossrefs

Bisection of A339820.

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

Cf. also A324651.

Sequence in context: A366170 A151732 A109554 * A269382 A253886 A253885

Adjacent sequences: A339818 A339819 A339820 * A339822 A339823 A339824

Keyword

nonn

Author

Antti Karttunen, Dec 18 2020

Status

approved