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A269871
Indices of square pyramidal numbers (A000330) that are the sum of 4 but no fewer nonzero squares.
0
5, 14, 21, 30, 37, 39, 40, 46, 53, 62, 69, 78, 85, 94, 101, 103, 104, 110, 117, 126, 133, 142, 149, 158, 159, 160, 165, 167, 168, 174, 181, 190, 197, 206, 213, 222, 229, 231, 232, 238, 245, 254, 261, 270, 277, 286, 293, 295, 296, 302, 309, 318, 325, 334, 341, 350, 357
OFFSET
1,1
COMMENTS
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.
Corresponding square pyramidal numbers are 55, 1015, 3311, 9455, 17575, 20540, 22140, 33511, 51039, 81375, 111895, 161239, 208335, 281295, 348551, 369564, ...
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, ...
EXAMPLE
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.
PROG
(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) ; }
for(n=0, 1e3, if(isA004215(n*(n+1)*(2*n+1)/6), print1(n, ", ")));
CROSSREFS
Sequence in context: A071317 A167201 A336145 * A323732 A048769 A190514
KEYWORD
nonn
AUTHOR
Altug Alkan, Mar 06 2016
STATUS
approved