The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 22 14:37 EDT 2020. Contains 337291 sequences. (Running on oeis4.)