A016032 Least positive integer that is the sum of two squares of positive integers in exactly n ways.

2, 50, 325, 1105, 8125, 5525, 105625, 27625, 71825, 138125, 5281250, 160225, 1221025, 2442050, 1795625, 801125, 446265625, 2082925, 41259765625, 4005625, 44890625, 30525625, 61051250, 5928325, 303460625, 53955078125, 35409725, 100140625, 1289367675781250

Offset

1,1

References

A. Beiler, Recreations in the Theory of Numbers, Dover, pp. 140-141.

Links

T. D. Noe and Ray Chandler, Table of n, a(n) for n = 1..2178 (a(2179) exceeds 1000 digits).

C. Rivera, Puzzle 62

Eric Weisstein's World of Mathematics, Square Number

G. Xiao, Two squares

Index entries for sequences related to sums of squares

Formula

a(n) = min(2*A018782(2n-1), A018782(2n), A018782(2n+1)).

Example

a(0) = 1 as 1 is the least positive integer not expressible as the sum of two squared positives.
a(1) = 2 from 2 = 1^2 + 1^2.
a(2) = 50 from 50 = 1^2 + 7^2 = 5^2 + 5^2.

Mathematica

Array[Block[{k = 1}, While[Length@ DeleteCases[PowersRepresentations[k, 2, 2], _?(! FreeQ[#, 0] &)] != #, k++]; k] &, 6] (* Michael De Vlieger, Mar 31 2019 *)

Prog

(PARI) b(k)=my(c=0); for(i=1, sqrtint(k\2), if(issquare(k-i^2), c+=1)); c \\ A025426
for(n=1, 10, k=1; while(k, if(b(k)==n, print1(k, ", "); break); k+=1)) \\ Derek Orr, Mar 20 2019

Crossrefs

Cf. A018825, A048610, A025284-A025293 (first entries).

See A000446, A124980 and A093195 for other versions.

Sequence in context: A226337 A048610 A007511 * A080299 A083939 A083941

Adjacent sequences: A016029 A016030 A016031 * A016033 A016034 A016035

Keyword

nonn,nice

Author

Robert G. Wilson v

Extensions

Corrected and extended by Jud McCranie

Definition improved by several correspondents, Nov 12 2007

Status

approved