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 A267321 Perfect powers that are not of the form x^2 + y^2 + z^2 where x, y and z are integers. 3
 343, 3375, 12167, 16807, 21952, 29791, 59319, 103823, 166375, 216000, 250047, 357911, 493039, 658503, 759375, 778688, 823543, 857375, 1092727, 1367631, 1404928, 1685159, 1906624, 2048383, 2460375, 2924207, 3442951, 3796416, 4019679, 4657463, 5359375, 6128487 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Perfect powers that are the sum of 4 but no fewer nonzero squares. See first comment in A004215. Intersection of A001597 and A004215. A134738 is a subsequence. Motivation for this sequence is the equation m^k = x^2 + y^2 + z^2 where x, y, z are integers and m > 0, k >= 2. Corresponding exponents are 3, 3, 3, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 3, 7, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 3, 3, 3, 3, 3, ... Numbers of the form (4^i*(8*j+7))^(2*k+3) where i,j,k>=0. - Robert Israel, Jan 14 2016 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 EXAMPLE 16807 is a term because 16807 = 7^5 and there is no integer values of x, y and z for the equation 7^5 = x^2 + y^2 + z^2. MAPLE N:= 10^10; # to get all terms <= N sort(convert({seq(seq(seq((4^i*(8*j+7))^(2*k+3),     k=0..floor(1/2*(log[4^i*(8*j+7)](N)-3))),      j = 0 .. floor((N^(1/3)*4^(-i)-7)/8)), i=0..floor(log[4](N^(1/3)/7)))}, list)); # Robert Israel, Jan 14 2016 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=1, 400, if(isA004215(n), print1(n, ", ") ; ) ; ) ; } for(n=0, 1e7, if(isA004215(n) && ispower(n), print1(n, ", "))); CROSSREFS Cf. A001597, A004215, A134738. Sequence in context: A250138 A016923 A016983 * A134738 A017151 A017247 Adjacent sequences:  A267318 A267319 A267320 * A267322 A267323 A267324 KEYWORD nonn AUTHOR Altug Alkan, Jan 13 2016 STATUS approved

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Last modified December 13 17:09 EST 2019. Contains 329970 sequences. (Running on oeis4.)