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 A138854 Numbers which are the sum of three cubes of distinct primes. 6
 160, 378, 476, 495, 1366, 1464, 1483, 1682, 1701, 1799, 2232, 2330, 2349, 2548, 2567, 2665, 3536, 3555, 3653, 3871, 4948, 5046, 5065, 5264, 5283, 5381, 6252, 6271, 6369, 6587, 6894, 6992, 7011, 7118, 7137, 7210, 7229, 7235, 7327, 7453, 8198, 8217, 8315 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This is a subset of A024975. The odd terms of this sequence are A138853, the even terms are 8+{ even terms of A120398 }. Thus primes in this sequence, A137365, are the same than primes in A138853. LINKS Chai Wah Wu, Table of n, a(n) for n = 1..10000 (terms 1..621 from R. J. Mathar) FORMULA A138854 = { p(i)^3+p(j)^3+p(k)^3 ; i>j>k>0 } = A138853 union { p(i)^3+p(j)^3+8 ; i>j>1} MAPLE isA030078 := proc(n)     local f ;     if n < 8 then         false;     else         f := ifactors(n)[2] ;         if nops(f) = 1 and op(2, op(1, f)) = 3 then             true;         else             false;         end if;     end if; end proc: isA138854 := proc(n)     local i, j, p, q, r, rcub ;     for i from 1 do         p := ithprime(i) ;         if p^3+(p+1)^3+(p+2)^3 > n then             return false;         end if;         for j from i+1 do             q := ithprime(j) ;             rcub := n-q^3-p^3 ;             if rcub <= q^3 then                 break;             fi ;             if isA030078(rcub) then                 return true;             end if;         end do:     end do: end proc: for n from 5 do     if isA138854(n) then         print(n);     end if; end do: # R. J. Mathar, Jun 09 2014 MATHEMATICA f[upto_]:=Module[{maxp=PrimePi[Floor[Power[upto, (3)^-1]]]}, Select[Union[Total/@(Subsets[Prime[Range[maxp]], {3}]^3)], #<=upto&]]; f[9000]  (* Harvey P. Dale, Mar 21 2011 *) PROG (PARI) isA138854(n)={ if( n%2, isA138853(n), isA120398(n-8)) } for( n=1, 10^4, isA138854(n) & print1(n", ")) CROSSREFS Cf. A024975 (a^3+b^3+c^3, a>b>c>0), A138853 (odd terms of this), A120398, A137365 (primes in A138853 / A138854). Sequence in context: A171225 A290463 A127338 * A133530 A278129 A184070 Adjacent sequences:  A138851 A138852 A138853 * A138855 A138856 A138857 KEYWORD nonn AUTHOR M. F. Hasler, Apr 13 2008 STATUS approved

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Last modified October 21 16:25 EDT 2019. Contains 328302 sequences. (Running on oeis4.)