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 A270820 Prime powers p^k (p prime, k > 1) that are not of the form x^2 + y^2 + z^2 where x, y and z are integers. 0
 343, 12167, 16807, 29791, 103823, 357911, 493039, 823543, 1092727, 2048383, 3442951, 4657463, 6436343, 6967871, 7880599, 11089567, 13651919, 18191447, 19902511, 28629151, 30080231, 40353607, 46268279, 49430863, 56181887, 80062991, 84604519, 99252847 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Proper prime powers that are the sum of 4 but no fewer nonzero squares. This sequence lists the numbers of the form A007522(n)^(2*k+1) where n,k > 0. Subsequence of A267321. Terms are 7^3, 23^3, 7^5, 31^3, 47^3, 71^3, 79^3, 7^7, 103^3, 127^3, 151^3, 167^3, 23^5, 191^3, 199^3, ... LINKS 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. MATHEMATICA nn = 120; Select[TakeWhile[Union@ Flatten@ Map[Prime[Range@ nn]^# &, Range[2, Floor[Log2[PrimePi@ nn]^2]]], # <= Prime[nn]^2 &], ! Resolve[Exists[{x, y, z}, Reduce[# == x^2 + y^2 + z^2, {x, y, z}, Integers]]] &] (* Michael De Vlieger, Mar 23 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) ; } forcomposite(n=4, 1e7, if(isA004215(n) && isprimepower(n), print1(n, ", "))); CROSSREFS Cf. A000961, A004215, A007522, A267321, A246547. Sequence in context: A277636 A224427 A134263 * A140250 A117197 A269554 Adjacent sequences:  A270817 A270818 A270819 * A270821 A270822 A270823 KEYWORD nonn AUTHOR Altug Alkan, Mar 23 2016 STATUS approved

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Last modified August 12 23:52 EDT 2022. Contains 356077 sequences. (Running on oeis4.)