

A052199


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


9



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
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OFFSET

1,2


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..94
Dirk FrettlĂ¶h, "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


EXAMPLE

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


PROG

(PARI)
c_old=1; for(n=1, 10000, c=0; for(i=1, floor(sqrt(n)), for(j=1, i1, if(i^2+j^2==n, c+=1))); if(c>c_old, print1(n, ", "); c_old=c))  Derek Orr, Mar 15 2019


CROSSREFS

Cf. A001983, A007511, A048610, A071383. Subsequence of A054994. Where records occur in A025441; corresponding number of ways is A060306.
Sequence in context: A234335 A071902 A211412 * A093195 A292228 A195579
Adjacent sequences: A052196 A052197 A052198 * A052200 A052201 A052202


KEYWORD

nonn


AUTHOR

Jud McCranie, Jan 28 2000


EXTENSIONS

More terms from Randall L. Rathbun, Jan 18 2002
Edited by Ray Chandler, Jan 12 2012


STATUS

approved



