A052199 Numbers that are expressible as the sum of 2 distinct positive squares in more ways than any smaller number.

1, 5, 65, 325, 1105, 5525, 27625, 71825, 138125, 160225, 801125, 2082925, 4005625, 5928325, 29641625, 77068225, 148208125, 243061325, 1215306625, 3159797225, 6076533125, 12882250225, 53716552825, 64411251125, 167469252925, 322056255625, 785817263725

Offset: 1

Author

Jud McCranie, Jan 28 2000

Keywords

• nonn

Examples

			65 = 1^2 + 8^2 = 4^2 + 7^2, the smallest expressible in two ways, so 65 is a term.
		

References

• Donald S. McDonald, Postings to sci.math newsgroup, Feb 21, 1995 and Dec 04, 1995.

Links

• Ray Chandler, Table of n, a(n) for n = 1..422
• Dirk Frettlöh, "Tile Orientations with Distinct Frequencies", Ch. 1.5 in Aperiodic Order, Vol. 2: Crystallography and Almost Periodicity, 2017, see page 9.
• Donald S. McDonald, World Mathematical Year 2000 Poster Competition
• G. Xiao, Two squares
• Index entries for sequences related to sums of squares

Crossrefs

Cf. A001983, A007511, A048610, A071383. Subsequence of A054994. Where records occur in A025441; corresponding number of ways is A060306.

Programs

PARI

c_old=-1;for(n=1,10000,c=0;for(i=1,floor(sqrt(n)),for(j=1,i-1,if(i^2+j^2==n,c+=1)));if(c>c_old,print1(n,", ");c_old=c)) \\ Derek Orr, Mar 15 2019

Extensions

More terms from Randall L Rathbun, Jan 18 2002

Edited by Ray Chandler, Jan 12 2012