A077116 n^3 - A065733(n).

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, 0, 152, 83, 48, 53, 104, 207, 7, 216, 100, 26, 0, 28, 116, 270, 496, 277, 104, 546, 503, 524, 615, 139, 368, 0, 391, 155, 732, 652, 648, 726, 55, 293, 631, 170, 704

Offset: 0

Author

Reinhard Zumkeller, Oct 29 2002

Keywords

• nonn
• easy

Comments

a(n) = 0 for n = m^2. - Zak Seidov, May 11 2007

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

Examples

			A065733(10) = 961 = 31^2 is the largest square less than or equal to 10^3 = 1000, therefore a(10) = 1000 - 961 = 39.
		

Crossrefs

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

Programs

Maple

A077116 := proc(n)
    A053186(n^3) ;
end proc: # R. J. Mathar, Jul 12 2016

Mathematica

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

PARI

A077116(n)=n^3-sqrtint(n^3)^2 \\ - M. F. Hasler, Sep 26 2013

Formula

a(n) = A154333(n) unless n is a square or, equivalently, a(n)=0. - M. F. Hasler, Oct 05 2013

a(n) = A053186(n^3). - R. J. Mathar, Jul 12 2016