1,2

Also least odd number with exactly n divisors. - Lekraj Beedassy (blekraj(AT)yahoo.com), Aug 30 2006

If n is prime, a(n)=3^(n-1). - Zak Seidov (zakseidov(AT)yahoo.com), Apr 18 2006

a(2n-1) = {1,9,81,729,225,59049,...} are the perfect squares. A122842[n] = Sqrt[ a(2n-1) ] = {1,3,9,27,15,243,729,45,6561,19683,135,177147,225,105,4782969,14348907,1215,...}. - Alexander Adamchuk (alex(AT)kolmogorov.com), Sep 13 2006

Also the least number k such that there are n partitions of k whose elements are consecutive integers. i.e.; 1=1, 3=1+2=3, 9=2+3+4=4+5=9, 15=1+2+3+4+5=4+5+6=7+8=15, etc. - Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 02 2007

The politeness of an integer, A069283(n), is defined to be the number of its nontrivial runsum representations, and the sequence 3, 9, 15, 81, 45, 729, 105, ... represents the least integers to have a politeness of 1, 2, 3, 4, ... This is also the sequence of smallest integers with n+1 odd divisors and so, apart from the leading 1, is precisely A038547. [From Ant King (mathstutoring(AT)ntlworld.com), Sep 23 2009]

Don Reble, Table of n, a(n) for n = 1..2000

T. Verhoeff, Rectangular and Trapezoidal Arrangements, J. Integer Sequences, Vol. 2, 1999, #99.1.6.

a(n) = A119265(n,n). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 11 2006

It was sugested by Alexander Adamchuk that for all n >= 1, we have a(3^(n-1)) = (p(n)#/2)^2 = (A002110(n)/2)^2 = A070826(n)^2. But this is false! E.g. (p(n)#/2)^2=3^2 5^2 7^2 ...23^2 29^2 does indeed have 3^9 odd factors, but it is greater than 3^8*5^2 7^2 ...23^2 which has 9*3*3*3*3*3*3*3 = 9*3^7=3^9 odd factors. - Richard Sabey, Oct 06 2007.

a(A053640(m)) = a(A000005(A053624(m))) = A053624(m). - Rick L. Shepherd (rshepherd2(AT)hotmail.com), Apr 20 2008

A122842 = Sqrt[ a(2n-1) ].

Cf. A001227, A005179, A002110, A070826.

Cf. A000005, A053640, A053624.

Sequence in context: A062804 A110960 A050869 this_sequence A083556 A015664 A134137

Adjacent sequences: A038544 A038545 A038546 this_sequence A038548 A038549 A038550

nonn,nice

Tom Verhoeff (Tom.Verhoeff(AT)acm.org)

Corrected by Ron Knott (R.Knott(AT)altavista.net), Feb 22, 2001.

a(30) from Zak Seidov (zakseidov(AT)yahoo.com), Apr 18 2006

a(32)-a(34) from Lekraj Beedassy (blekraj(AT)yahoo.com), Aug 30 2006