A180149 Integers with precisely two partitions into sums of four squares of nonnegative numbers.

4, 9, 10, 12, 13, 16, 17, 19, 20, 21, 22, 29, 30, 31, 35, 39, 40, 44, 46, 47, 48, 64, 71, 80, 88, 120, 160, 176, 184, 192, 256, 320, 352, 480, 640, 704, 736, 768, 1024, 1280, 1408, 1920, 2560, 2816, 2944, 3072, 4096, 5120, 5632, 7680

Offset: 1

Author

Ant King, Aug 17 2010

Keywords

• easy
• nonn

Comments

The largest odd member of this sequence is 71, and from a(32)=320 onwards the terms satisfy the eighth-order recurrence relation a(n)=4a(n-8).

A002635(a(n)) = 2. - Reinhard Zumkeller, Jul 13 2014

Examples

			As the fifth integer which has precisely two partitions into sums of four squares of nonnegative numbers is 13, then a(5)=13.
		

Links

• Robert Price, Table of n, a(n) for n = 1..65
• D. H. Lehmer, On the Partition of Numbers into Squares, The American Mathematical Monthly, Vol. 55, No.8, October 1948, pp. 476-481.
• Index entries for sequences related to sums of squares

Crossrefs

Cf. A002635, A006431, A245022.

Programs

Haskell

a180149 n = a180149_list !! (n-1)
a180149_list = filter ((== 2) . a002635) [0..]
-- Reinhard Zumkeller, Jul 13 2014

Mathematica

Select[Range[10000], Length[PowersRepresentations[ #, 4, 2]]==2&]

Formula

The members of this sequence are {9, 13, 17, 19, 21, 29, 30, 31, 35, 39, 46, 47, 71} together with all integers of the form 5*2^N, 11*2^N and {1,3,30,46}*4^N where N > 0 (which includes a necessary correction to Lehmer's result).