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A126704
Prime numbers that are the sum of three distinct positive sixth powers.
1
4889, 50753, 51481, 66377, 262937, 308801, 797681, 840241, 1000793, 1046657, 1772291, 2303003, 2986777, 3032641, 3107729, 3365777, 4757609, 4804201, 5135609, 7530329, 7534361, 8061041, 8065073, 10516249, 12394721, 14638753
OFFSET
1,1
LINKS
EXAMPLE
4889 = 2^6 + 3^6 + 4^6 = 64 + 729 + 4096.
66377 = 4^6 + 5^6 + 6^6 = 4096 + 15625 + 46656.
MAPLE
N:= 10^10; # to find all terms <= N
A := {}:
for a from 1 to iroot(N, 6) do
for b from 1 to a-1 while a^6 + b^6 < N do
for c from (a+b) mod 2 + 1 to b-1 by 2 do
r:= a^6 + b^6 + c^6;
if r > N then break fi;
if isprime(r) then A:= A union {r} fi;
od od od:
sort(convert(A, list)); # Robert Israel, Dec 15 2015
MATHEMATICA
Union[Select[Total/@Subsets[Range[20]^6, {3}], PrimeQ]] (* Harvey P. Dale, Apr 20 2013 *)
PROG
(PARI) {m=16; p=m^6; w=[]; for(i=1, m-2, for(j=i+1, m-1, for(k=j+1, m, if((n=i^6+j^6+k^6)<p&&isprime(n), w=concat(w, n))))); w=vecsort(w); for(h=1, #w, print1(w[h], ", "))} /* Klaus Brockhaus, Feb 16 2007 */
CROSSREFS
KEYWORD
nonn
AUTHOR
Tomas Xordan, Feb 11 2007
EXTENSIONS
Edited, corrected and extended by Klaus Brockhaus, Feb 16 2007
STATUS
approved