A212641 - OEIS

%I #14 Jul 14 2019 10:57:50

%S 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,

%T 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,

%U 49,5,3,81,27,45,17,21,55,3,27,7,3,13,45,15,105,9,45

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

%C 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.

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

%C Each odd integer appears an infinite number of times.

%H Amiram Eldar, <a href="/A212641/b212641.txt">Table of n, a(n) for n = 1..10000</a>

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

%e 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.

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

%K nonn

%O 1,2

%A _Matthew Vandermast_, Jun 09 2012