A212641 Largest odd divisor of A212640(n) (number of divisors of n-th powerful number that is the first integer of its prime signature).

1, 3, 1, 5, 3, 9, 7, 3, 1, 15, 1, 9, 9, 5, 5, 21, 3, 27, 11, 3, 25, 7, 9, 3, 27, 15, 1, 45, 13, 15, 35, 3, 9, 27, 9, 7, 33, 5, 15, 5, 63, 21, 15, 9, 45, 9, 1, 11, 9, 3, 75, 1, 39, 25, 21, 81, 49, 5, 3, 81, 27, 45, 17, 21, 55, 3, 27, 7, 3, 13, 45, 15, 105, 9, 45

Offset

1,2

Comments

The odd part of d(n), or largest odd divisor of d(n) (A212181(n)), is a function of the second signature of n (cf. A212172). Since A181800 gives the first integer of each second signature, this sequence gives the value of A212181 for each second signature in order of its first appearance.

Note: The odd part of d(n) is not the same as the number of odd divisors of n (A001227(n)).

Each odd integer appears an infinite number of times.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) = A000265(A212640(n)) = A212181(A181800(n)).

Example

A181800(5) = 32 has 6 divisors (1, 2, 4, 8, 16 and 32).  The largest odd divisor of 6 is 3. Hence, a(5) = 3.

Crossrefs

Cf. A000005, A000265, A181800, A212172, A212181, A212640.

Sequence in context: A333871 A364034 A373079 * A195835 A077881 A129095

Adjacent sequences: A212638 A212639 A212640 * A212642 A212643 A212644

Keyword

nonn

Author

Matthew Vandermast, Jun 09 2012

Status

approved