1,3

If n is of the form 4^i*(8j+7) (where i>=0, j>=0) then n^3 is not in the sequence because n^3 is of the mentioned form so n^3 is in A004215 hence according to the definition n^3 is not in this sequence (see formula for A004215). Hence 7^3, 15^3, 23^3, 28^3, 31^3, 39^3, ... are not in the sequence. Is there a number n such that n^3 is not in the sequence but n is not of the form 4^i*(8j+7)? - Farideh Firoozbakht (mymontain(AT)yahoo.com), Nov 23 2006

A number n^3 belongs to this sequence iff and only n is sum of three squeres. Proof is immediate from Catalan's identity (x^2+y^2+z^2)^3=(x^2(3z^2-x^2-y^2))^2+(y^2(3z^2-x^2-y^2))^2+(z^2(z^2-3x^2-3y^2))^2. - Artur Jasinski (grafix(AT)csl.pl), Dec 09 2006

a(n) = A000378(n)^3.

Equals A000578 INTERSECT A000378.

125 is in the sequence because 125=5^3=0^2+2^2+11^2=0^2+5^2+10^2= 3^2+4^2+10^2=5^2+6^2+8^2.

27=3^3=1^2+1^2+5^2. 125=5^3=2^2+0^2+11^2. 216=6^3=4^2+2^2+14^2.

Needs["NumberTheory`NumberTheoryFunctions`"]; Select[Range[0, 50]^3, SumOfSquaresR[3, # ] > 0 &] (*Chandler*)

(PARI) isA125084(n)={ local(cnt, a, b) ; cnt=0 ; a=0; while(a^2<=n, b=0 ; while(b<=a && a^2+b^2<=n, if(issquare(n-a^2-b^2), return(1) ) ; b++ ; ) ; a++ ; ) ; return(0) ; } { for(n=1, 300, if(isA125084(n^3), print1(n^3, ", ") ; ) ; ) ; } (Mathar)

Cf. A004215.

Sequence in context: A014187 A050750 A100571 this_sequence A052048 A052064 A125496

Adjacent sequences: A125081 A125082 A125083 this_sequence A125085 A125086 A125087

nonn

Artur Jasinski (grafix(AT)csl.pl), Nov 20 2006, Nov 21 2006, Nov 22 2006

Corrected and extended by Farideh Firoozbakht (mymontain(AT)yahoo.com), Ray Chandler (rayjchandler(AT)sbcglobal.net) and R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 23 2006