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%I #9 Mar 07 2016 12:56:13
%S 5,14,21,30,37,39,40,46,53,62,69,78,85,94,101,103,104,110,117,126,133,
%T 142,149,158,159,160,165,167,168,174,181,190,197,206,213,222,229,231,
%U 232,238,245,254,261,270,277,286,293,295,296,302,309,318,325,334,341,350,357
%N Indices of square pyramidal numbers (A000330) that are the sum of 4 but no fewer nonzero squares.
%C In other words, integers n such that equation 1^2 + 2^2 + ... + n^2 = x^2 + y^2 + z^2 where x, y and z are integers is not soluble.
%C Corresponding square pyramidal numbers are 55, 1015, 3311, 9455, 17575, 20540, 22140, 33511, 51039, 81375, 111895, 161239, 208335, 281295, 348551, 369564, ...
%C Initial terms of first differences of this sequence are 9, 7, 9, 7, 2, 1, 6, 7, 9, 7, 9, 7, 9, 7, 2, 1, 6, 7, 9, 7, 9, 7, ...
%e 5 is a term because A000330(5) = 55 and the equation 55 = x^2 + y^2 + z^2 where x, y, z are integers is not soluble.
%o (PARI) isA004215(n) = { my(fouri, j) ; fouri=1 ; while( n >=7*fouri, if( n % fouri ==0, j= n/fouri -7 ; if( j % 8 ==0, return(1) ) ; ) ; fouri *= 4 ; ) ; return(0) ; }
%o for(n=0, 1e3, if(isA004215(n*(n+1)*(2*n+1)/6), print1(n, ", ")));
%Y Cf. A000330, A004215.
%K nonn
%O 1,1
%A _Altug Alkan_, Mar 06 2016
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