A339972 - OEIS

%I #12 Feb 09 2021 21:42:54

%S 1,3,5,15,3,9,15,45,1,3,5,15,3,9,15,45,9,27,45,135,27,81,135,405,9,27,

%T 45,135,27,81,135,405,11,33,55,165,33,99,165,495,11,33,55,165,33,99,

%U 165,495,99,297,495,1485,297,891,1485,4455,99,297,495,1485,297,891,1485,4455,7,21,35,105,21,63,105,315,7,21

%N Odd part of phi(A019565(8*n)).

%C Compare also to the scatter plots of A339898 and A339901.

%H Antti Karttunen, <a href="/A339972/b339972.txt">Table of n, a(n) for n = 0..16383</a>

%F If 16n = 2^e1 + 2^e2 + ... + 2^ek [e1 ... ek distinct], then a(n) = A057023(e1) * A057023(e2) * ... * A057023(ek).

%F a(n) = A339971(4*n) = A000265(A339821(4*n)) = A053575(A019565(8*n)).

%o (PARI)

%o A000265(n) = (n>>valuation(n, 2));

%o A339972(n) = { my(m=1, p=5); while(n>0, p = nextprime(1+p); if(n%2, m *= A000265(p-1)); n >>= 1); (m); };

%Y Quadrisection of A339971.

%Y Cf. A000265, A019565, A057023, A053575, A339821, A339898, A339901.

%K nonn,look

%O 0,2

%A _Antti Karttunen_, Dec 26 2020