cp's OEIS Frontend

A222949 Numbers that are a sum of four nonzero squares where the summands have no common square factor > 1.

%I A222949 #14 Dec 12 2015 21:37:30
%S A222949 4,7,10,12,13,15,18,19,20,21,22,23,25,26,27,28,30,31,33,34,35,36,37,
%T A222949 38,39,42,43,44,45,46,47,49,50,51,52,53,54,55,57,58,59,60,61,62,63,65,
%U A222949 66,67,68,69,70,71,73,74,75,76,77,78,79,81,82,83,84,85,86,87,89,90,91,92,93,94,95,97,98,99,100,101,102
%N A222949 Numbers that are a sum of four nonzero squares where the summands have no common square factor > 1.
%C A222949 A representation of a(n) as a sum of four nonzero squares is denoted by [s(1),s(2),s(3),s(4)] with nondecreasing entries > 1 and Sum_{j=1..4} s(j)^2 = a(n). It is called primitive if gcd(s(1),s(2),s(3),s(4)) = 1. a(n) is the number with at least one such primitive representation for n, and the multiplicity m is given by the non-vanishing entries of A097203, that is A097203(a(n)).
%F A222949 A097203(a(n)) is not 0.
%e A222949 a(1) = 4 because 4 has the primitive representation [1, 1, 1, 1].
%e A222949 a(16) = 28, because 28 has the primitive representations [1, 1, 1, 5] and [1, 3, 3, 3] ([2, 2, 2, 4] is not primitive.).
%e A222949 4: [1, 1, 1, 1], 7: [1, 1, 1, 2], 10: [1, 1, 2, 2], 12: [1, 1, 1, 3], 13: [1, 2, 2, 2], 15: [1, 1, 2, 3], 18: [1, 2, 2, 3],
%e A222949   19: [1, 1, 1, 4], 20: [1, 1, 3, 3], 21: [2, 2, 2, 3], 22: [1, 1, 2, 4], 23: [1, 2, 3, 3], 25: [1, 2, 2, 4],  26: [2, 2, 3, 3], 27: [1, 1, 3, 4], 28: [1, 1, 1, 5], [1, 3, 3, 3], ...
%Y A222949 Cf. A097203.
%K A222949 nonn
%O A222949 1,1
%A A222949 _Wolfdieter Lang_, Mar 25 2013