The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A099426 Numbers n where n^2 = x^3 + y^3; x,y>0 and gcd(x,y)=1. 7
 3, 228, 671, 1261, 6371, 9765, 35113, 35928, 40380, 41643, 66599, 112245, 124501, 127499, 167160, 191771, 205485, 255720, 297037, 377567, 532392, 546013, 647569, 681285, 812340, 897623, 1043469, 1125683, 1261491, 1431793, 1433040, 1584828, 1783067, 1984009, 2107391, 2372903, 2440893, 2484469, 2548557 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Based on an observation of Ed Pegg Jr, who supplied terms a(2)-a(6) and a(8). LINKS Joerg Arndt and Donovan Johnson, Table of n, a(n) for n = 1..300 (first 55 terms from Joerg Arndt) EXAMPLE 228 is in the sequence because 228^2 = 11^3 + 37^3 and gcd(11, 37) = 1. MATHEMATICA n = 10^7; n2 = n^2; x = 1; x3 = x^3; Reap[ While[x3 < n2, y = x + 1; y3 = y^3; While[y3 < n2, If[GCD[x, y] == 1, s = x3 + y3; If[ IntegerQ[r = Sqrt[s]], Print[r]; Sow[r]; Break[]]]; y += 1; y3 = y^3]; x += 1; x3 = x^3]][[2, 1]] // Sort (* Jean-François Alcover, Jan 11 2013, translated from Joerg Arndt's 2nd Pari program *) PROG (PARI) is_A099426(n)= {     my(n2=n^2, k=1, k3=1, r);     while( k3 < n2,         if ( ispower(n2-k3, 3, &r),             if ( gcd(r, k)==1, return(1) );         );         k+=1;  k3=k^3;     );     return(0); } for (n=1, 10^8, if( is_A099426(n), print1(n, ", ")) ); /* Joerg Arndt, Sep 30 2012 */ (PARI) /* compute all terms below a threshold at once, terms need to be sorted */ { N = 10^7; N2 = N^2; x=1; x3=x^3; while ( x3 < N2,     y=x+1; y3=y^3;     while ( y3 < N2,         if ( gcd(x, y) == 1,             s = x3 + y3;             if ( issquare(s, &r), print(r); break(); );         );         y+=1;  y3 = y^3;     );     x+=1;  x3 = x^3; ); } /* Joerg Arndt, Sep 30 2012 */ (PARI) for(s=2, 1e5, for(x=1, s\2, my(y=s-x); if(gcd(x, y)>1, next); if(issquare(x^3+y^3), print1(s", ")))) \\ Charles R Greathouse IV, Nov 06 2014 CROSSREFS Cf. A099532, A099533, A103255 (min(x,y), sorted). Sequence in context: A131493 A228871 A195500 * A332123 A100201 A159807 Adjacent sequences:  A099423 A099424 A099425 * A099427 A099428 A099429 KEYWORD nonn AUTHOR Hans Havermann, Oct 15 2004 EXTENSIONS More terms from Hans Havermann and Bodo Zinser, Oct 20 2004 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 12 10:58 EDT 2021. Contains 344947 sequences. (Running on oeis4.)