cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A077116 n^3 - A065733(n).

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%I A077116 #28 Jul 12 2016 12:11:29
%S A077116 0,0,4,2,0,4,20,19,28,0,39,35,47,81,40,11,0,13,56,135,79,45,39,67,135,
%T A077116 0,152,83,48,53,104,207,7,216,100,26,0,28,116,270,496,277,104,546,503,
%U A077116 524,615,139,368,0,391,155,732,652,648,726,55,293,631,170,704
%N A077116 n^3 - A065733(n).
%C A077116 a(n) = 0 for n = m^2. - _Zak Seidov_, May 11 2007
%C A077116 It has been asked whether some primes do not occur in this sequence. It seems indeed that primes 3, 5, 17, 23, 29, 31, 37, 41, 43, 59, 61,... do not occur, primes 2, 7, 11, 13, 19, 47, 53, 67, 79, 83,... do. For further investigations, see A087285 = the range of this sequence, and also the related sequences A229618 = range of A181138, and A165288. - _M. F. Hasler_, Sep 26 2013 and Oct 05 2013
%F A077116 a(n) = A154333(n) unless n is a square or, equivalently, a(n)=0. - _M. F. Hasler_, Oct 05 2013
%F A077116 a(n) = A053186(n^3). - _R. J. Mathar_, Jul 12 2016
%e A077116 A065733(10) = 961 = 31^2 is the largest square less than or equal to 10^3 = 1000, therefore a(10) = 1000 - 961 = 39.
%p A077116 A077116 := proc(n)
%p A077116     A053186(n^3) ;
%p A077116 end proc: # _R. J. Mathar_, Jul 12 2016
%t A077116 Table[c = n^3; c - Floor[Sqrt[c]]^2, {n, 0, 200}] (* _Vladimir Joseph Stephan Orlovsky_, Jun 02 2011 *)
%o A077116 (PARI) A077116(n)=n^3-sqrtint(n^3)^2 \\ - _M. F. Hasler_, Sep 26 2013
%Y A077116 Cf. A000578, A070929, A077118, A077119, A075847.
%K A077116 nonn,easy
%O A077116 0,3
%A A077116 _Reinhard Zumkeller_, Oct 29 2002