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A224772 Multiplicities for representations of numbers as primitive sums of three distinct nonzero squares. 2
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 2, 0, 0, 1, 1, 0, 0, 2, 1, 0, 0, 0, 2, 1, 0, 2, 1, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 2, 2, 1, 0, 1, 2, 0, 0, 0, 2, 0, 0, 3, 0, 0, 0, 2, 1, 1, 0, 1, 3, 0, 0, 1, 1, 1, 0, 2, 1, 0, 0, 1, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, 0, 1, 3, 0, 0, 1, 2, 1, 0, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,62

COMMENTS

a(n) = k, for n >= 1, if there are exactly k representations of n as a primitive sum of three distinct nonzero squares. If a(n) = 0 then n has no such representation.

The increasingly ordered numbers with a(n) > 0 are given in A224771.

LINKS

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

FORMULA

a(n) = k if n = a^2 + b^2 + c^2, a, b, and c integers, 0 < a <  b < c and gcd(a,b,c) = 1, for exactly k different triples (a, b, c). If there is no such triple then a(n) = 0.

EXAMPLE

a(14) = 1 because the first number with a representation in question, denoted by a triple (a, b, c), is 14, with the unique triple (1, 2, 3).

a(62) = 2 for the first number 62 which has two representations, denoted by (1, 5, 6) and (2, 3, 7).

a(101) = 3 for the first number 101 with three triples, namely (1, 6, 8), (2, 4, 9) and (4, 6, 7).

MATHEMATICA

nn = 10; t = Table[0, {nn^2}]; Do[If[GCD[a, b, c] == 1, n = a^2 + b^2 + c^2; If[n <= nn^2, t[[n]]++]], {a, nn}, {b, a + 1, nn}, {c, b + 1, nn}]; t (* T. D. Noe, Apr 20 2013 *)

CROSSREFS

Cf. A224771, A025442 (multiplicities for sums of three distinct nonzero squares).

Sequence in context: A281457 A159708 A144625 * A025442 A260118 A128582

Adjacent sequences:  A224769 A224770 A224771 * A224773 A224774 A224775

KEYWORD

nonn

AUTHOR

Wolfdieter Lang, Apr 19 2013

STATUS

approved

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Last modified April 17 16:59 EDT 2021. Contains 343063 sequences. (Running on oeis4.)