A122842 Square roots of the odd indexed terms of A038547.

1, 3, 9, 27, 15, 243, 729, 45, 6561, 19683, 135, 177147, 225, 105, 4782969, 14348907, 1215, 675, 387420489, 3645, 3486784401, 10460353203, 315, 94143178827, 3375, 32805, 2541865828329, 6075, 98415, 68630377364883

Offset: 1

Author

Alexander Adamchuk, Sep 13 2006, Sep 25 2006

Keywords

• nonn

Comments

A038547(n) is the least number with exactly n odd divisors. For odd n these are perfect squares.

Examples

			a(1) = 1 because A038547(1) = 1.
a(2) = 3 because A038547(3) = 9.
a(5) = 15 because A038547(9) = 225.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..2100 (terms 1..1000 from R. J. Mathar)

Crossrefs

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

Cf. A007051, A070826, A002110.

Programs

Mathematica

(* Function a038547[ ] is defined in A038547 *)
a122842[n_]:=Sqrt[a038547[2n-1]]
Map[a122842,Range[30]] (* Hartmut F. W. Hoft, Feb 07 2023 *)

Formula

a(n) = sqrt(A038547(2*n-1)).

a(n) = sqrt(A119265(2*n-1, 2*n-1)).

a(n) = 3^(n-1) for n = (p+1)/2, where p is an odd prime.

a(3*n+2) = 5*3^n for n = (p-1)/2, where p is an odd prime.

Extensions

More terms from R. J. Mathar, Sep 20 2006

Edited by Hartmut F. W. Hoft, Feb 07 2023