A004432 - OEIS

A004432

Numbers that are the sum of 3 distinct nonzero squares.

14, 21, 26, 29, 30, 35, 38, 41, 42, 45, 46, 49, 50, 53, 54, 56, 59, 61, 62, 65, 66, 69, 70, 74, 75, 77, 78, 81, 83, 84, 86, 89, 90, 91, 93, 94, 98, 101, 104, 105, 106, 107, 109, 110, 113, 114, 115, 116, 117, 118, 120, 121, 122, 125, 126, 129, 131, 133

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OFFSET

1,1

COMMENTS

Numbers that can be written as a(n) = x^2 + y^2 + z^2 with 0 < x < y < z.

This is a subsequence (equal to the range) of A024803. As a set, it is the union of A025339 and A024804, subsequences of numbers having exactly one, resp. more than one, such representations. - M. F. Hasler, Jan 25 2013

Conjecture: a number n is a sum of 3 squares, but not a sum of 3 distinct nonzero squares (i.e., is in A004432 but not A000408), if and only if it is of the form 4^j*s, where j >= 0 and s in {1, 2, 3, 5, 6, 9, 10, 11, 13, 17, 18, 19, 22, 25, 27, 33, 34, 37, 43, 51, 57, 58, 67, 73, 82, 85, 97, 99, 102, 123, 130, 163, 177, 187, 193, 267, 627, 697}. - Jeffrey Shallit, Jan 15 2017

4*a(n) gives the sums of 3 distinct nonzero even squares. - Wesley Ivan Hurt, Apr 05 2021

LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000

Index entries for sequences related to sums of squares

FORMULA

A004432 = { x^2 + y^2 + z^2; 0 < x < y < z }.

n is in A004432 <=> A025442(n) > 0. - M. F. Hasler, Feb 03 2013

EXAMPLE

14 = 1^2 + 2^2 + 3^2;

62 = 1^2 + 5^2 + 6^2.

MATHEMATICA

f[upto_]:=Module[{max=Floor[Sqrt[upto]]}, Select[Union[Total/@ (Subsets[ Range[ max], {3}]^2)], #<=upto&]]; f[150] (* Harvey P. Dale, Mar 24 2011 *)