A339971 Odd part of A339821(n).

1, 1, 1, 1, 3, 3, 3, 3, 5, 5, 5, 5, 15, 15, 15, 15, 3, 3, 3, 3, 9, 9, 9, 9, 15, 15, 15, 15, 45, 45, 45, 45, 1, 1, 1, 1, 3, 3, 3, 3, 5, 5, 5, 5, 15, 15, 15, 15, 3, 3, 3, 3, 9, 9, 9, 9, 15, 15, 15, 15, 45, 45, 45, 45, 9, 9, 9, 9, 27, 27, 27, 27, 45, 45, 45, 45, 135, 135, 135, 135, 27, 27, 27, 27, 81, 81, 81, 81, 135

Offset: 0

Author

Antti Karttunen, Dec 26 2020

Keywords

• nonn

Crossrefs

Cf. A000010, A000265, A003961, A019565, A053575, A057023, A336466, A339821, A339822, A339970.

Cf. A339972 (quadrisection).

Programs

PARI

A000265(n) = (n>>valuation(n,2));
A339971(n) = { my(m=1, p=2); while(n>0, p = nextprime(1+p); if(n%2, m *= A000265(p-1)); n >>= 1); (m); };

Formula

If 4n = 2^e1 + 2^e2 + ... + 2^ek [e1 ... ek distinct], then a(n) = A057023(e1) * A057023(e2) * ... * A057023(ek).

a(n) = A053575(A019565(2n)) = A336466(A003961(A019565(n))) = A000265(A339821(n)).

a(n) = A339821(n) / A000079(A339822(n)).