A077116 - OEIS

%I #28 Jul 12 2016 12:11:29

%S 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 0,152,83,48,53,104,207,7,216,100,26,0,28,116,270,496,277,104,546,503,

%U 524,615,139,368,0,391,155,732,652,648,726,55,293,631,170,704

%N n^3 - A065733(n).

%C a(n) = 0 for n = m^2. - _Zak Seidov_, May 11 2007

%C 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 a(n) = A154333(n) unless n is a square or, equivalently, a(n)=0. - _M. F. Hasler_, Oct 05 2013

%F a(n) = A053186(n^3). - _R. J. Mathar_, Jul 12 2016

%e 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 := proc(n)

%p     A053186(n^3) ;

%p end proc: # _R. J. Mathar_, Jul 12 2016

%t Table[c = n^3; c - Floor[Sqrt[c]]^2, {n, 0, 200}] (* _Vladimir Joseph Stephan Orlovsky_, Jun 02 2011 *)

%o (PARI) A077116(n)=n^3-sqrtint(n^3)^2 \\ - _M. F. Hasler_, Sep 26 2013

%Y Cf. A000578, A070929, A077118, A077119, A075847.

%K nonn,easy

%O 0,3

%A _Reinhard Zumkeller_, Oct 29 2002