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 A135912 Number of 5-tuples (x,y,z,t,u) of nonnegative integers such that x^2+y^3+z^4+t^5+u^6 = n. 4
 1, 5, 10, 10, 6, 5, 6, 4, 2, 5, 10, 10, 6, 4, 3, 1, 2, 9, 15, 11, 4, 3, 3, 1, 2, 8, 13, 12, 10, 9, 5, 2, 5, 12, 15, 9, 5, 10, 12, 6, 3, 7, 10, 9, 10, 11, 6, 2, 4, 10, 14, 10, 8, 11, 8, 2, 2, 7, 10, 9, 9, 7, 2, 2, 9, 21, 26, 16, 9, 13, 11, 3, 3, 11, 16, 12, 9, 9, 5, 3, 8, 21, 29, 21, 14, 12, 7, 3, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(n) > 0 for n <= 10000. Is there any n for which a(n) = 0? Note that there are many famous hard problems connected with sequences A045634, A135910, A135911 and the present entry (see the Ford reference). The graph of this sequence suggests that a(n) is never zero. Checked to 10^5. - T. D. Noe, Mar 07 2008 LINKS T. D. Noe, Table of n, a(n) for n = 0..10000 K. B. Ford, The representation of numbers as sums of unlike powers II, J. Amer. Math. Soc., 9 (1996), 919-940. MAPLE M:=100; M2:=M^2; t0:=array(0..M2); for i from 0 to M2 do t0[i]:=0; od: for a from 0 to M do na:=a^2; for b from 0 to M do nb:=na+b^3; if nb <= M2 then for c from 0 to M do nc:=nb+c^4; if nc <= M2 then for d from 0 to M2 do nd:=nc+d^5; if nd <= M2 then for e from 0 to M2 do i:=nd+e^6; if i <= M2 then t0[i]:=t0[i]+1; fi; od: fi; od; fi; od: fi; od: od: [seq(t0[i], i=0..M2)]; for i from 0 to M2 do if t0[i]=0 then lprint(i); fi; od: CROSSREFS Cf. A045634, A135910, A135911. Sequence in context: A321357 A065755 A346007 * A200990 A040020 A222181 Adjacent sequences: A135909 A135910 A135911 * A135913 A135914 A135915 KEYWORD nonn AUTHOR N. J. A. Sloane, Mar 07 2008 STATUS approved

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Last modified August 8 04:35 EDT 2024. Contains 375018 sequences. (Running on oeis4.)