A016032 - OEIS

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, 52073125

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

REFERENCES

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

Elena Deza and Michel Marie Deza, Figurate numbers, World Scientific Publishing (2012), page 435.

LINKS

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

Carlos Rivera, Puzzle 62. The qs-sequence, (by T.W.A. Baumann), The Prime Puzzles & Problems Connection.

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

(PARI) a(n) = vecmin([2*A018782(2*n-1), A018782(2*n), A018782(2*n+1)]); \\ Michel Marcus, Sep 22 2025

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