1,2

A038547[n] is least number with exactly n odd divisors. It appears that for n>1 a(n) is divisible by 3^m where m(n) = {0,1,2,3,1,5,6,2,8,9,3,11,2,1,14,15,5,...}. a(n) = 3^(n-1) for n = (p+1)/2, where p is odd prime.

a(3k+2) = 5*3^k for k = {1,2,3,5,6,8,9,11,14,15,...} = A005097[n] (Odd primes - 1)/2. Thus a(3(p-1)/2 + 2) = 5*3^((p-1)/2). a(9k+5) = 3^k*5*7 for k ={1,2,3,5,...}. 3 divides a(2), 5 divides a(5), 7 divides a(14), 11 divides a(41), 13 divides a(122), etc. The first occurrence of the odd prime divisor Prime[n] among divisors of a(n) occurs at n = {2,5,14,41,122,...} = A007051[n-1] = (3^(n-1) + 1)/2 for n>1. Thus a(A007051[n-1]) = A070826[n] or a(3^(n-1) + 1)/2) = p(n)#/2 = A002110[n]/2 for n>1.

R. J. Mathar, Table of n, a(n) for n = 1..1000

a(n) = Sqrt[ A038547[2n-1] ]. a(n) = Sqrt[ A119265[2n-1,2n-1] ].

A038547[n] begins {1,3,9,15,81,45,729,105,225,405,59049,315,...}.

a(1) = 1 because A038547(1) = 1.

a(2) = 3 because A038547(3) = 9.

a(5) = 15 because A038547(9) = 225.

Cf. A038547, A121858, A001227, A005179, A119265.

Cf. A007051, A070826, A002110.

Sequence in context: A070345 A070359 A131997 this_sequence A070358 A036123 A070344

Adjacent sequences: A122839 A122840 A122841 this_sequence A122843 A122844 A122845

nonn

Alexander Adamchuk (alex(AT)kolmogorov.com), Sep 13 2006, Sep 25 2006

More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 20 2006