A001948 -id:A001948

Search: a001948 -id:a001948

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A001944

Numbers that are the sum of 4 distinct squares: of form w^2 + x^2 + y^2 + z^2 with 0 <= w < x < y < z.

+10
5

14, 21, 26, 29, 30, 35, 38, 39, 41, 42, 45, 46, 49, 50, 51, 53, 54, 56, 57, 59, 61, 62, 63, 65, 66, 69, 70, 71, 74, 75, 77, 78, 79, 81, 83, 84, 85, 86, 87, 89, 90, 91, 93, 94, 95, 98, 99, 101, 102, 104, 105, 106, 107, 109, 110, 111, 113, 114, 115, 116, 117

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

OFFSET

1,1

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

Index entries for sequences related to sums of squares

EXAMPLE

14 = 0^2 + 1^2 + 2^2 + 3^2.

MATHEMATICA

nn = 20; Select[Union[Flatten[Table[a^2 + b^2 + c^2 + d^2, {a, 0, nn}, {b, a + 1, nn}, {c, b + 1, nn}, {d, c + 1, nn}]]], # <= nn^2 &] (* T. D. Noe, Aug 17 2012 *)

CROSSREFS

Cf. A001974, A001983, A001948, A001995.

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

A243582

Integers of the form 8k+7 (A004771) that cannot be written as sum of four distinct squares.

+10
5

7, 15, 23, 31, 47, 55, 103

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

OFFSET

1,1

LINKS

Table of n, a(n) for n=1..7.

J. O. Sizemore, Lagrange's Four Square Theorem

R. C. Vaughan, Lagrange's four-square theorem

Eric Weisstein's World of Math, Lagrange's Four-Square Theorem

Wikipedia, Lagrange's four-square theorem

EXAMPLE

a(6) = 55 since 55 == 7 (mod 8) and all its representations as a sum of squares have duplicates, namely, 55=1^2+1^2+2^2+7^2, 55=1^2+2^2+5^2+5^2, 55=1^2+3^2+3^2+6^2.

CROSSREFS

Cf. A001948, A004771, A008586, A016813, A016825, A004767, A243577, A243578, A243579, A243580, A243581.

KEYWORD

nonn,fini,full

AUTHOR

Walter Kehowski, Jun 08 2014

STATUS

approved

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