A339972 Odd part of phi(A019565(8*n)).

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

Offset: 0

Author

Antti Karttunen, Dec 26 2020

Keywords

• nonn
• look

Comments

Compare also to the scatter plots of A339898 and A339901.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..16383

Crossrefs

Quadrisection of A339971.

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

Programs

PARI

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

Formula

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

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