A003362 - OEIS

%I #35 Mar 27 2022 16:26:20

%S 6,69,132,195,258,321,384,734,797,860,923,986,1049,1462,1525,1588,

%T 1651,1714,2190,2253,2316,2379,2918,2981,3044,3646,3709,4101,4164,

%U 4227,4290,4353,4374,4416,4829,4892,4955,5018,5081,5557,5620,5683,5746,6285,6348,6411,7013

%N Numbers that are the sum of 6 positive 6th powers.

%C This sequence has no sixth powers less than 1.5133*10^35. - _J. Lowell_, Jul 03 2021

%H David A. Corneth, <a href="/A003362/b003362.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from T. D. Noe)

%e From _David A. Corneth_, Aug 03 2020: (Start)

%e 448832 is in the sequence as 448832 = 2^6 + 6^6 + 6^6 + 6^6 + 6^6 + 8^6.

%e 1000733 is in the sequence as 1000733 = 1^6 + 1^6 + 1^6 + 1^6 + 3^6 + 10^6.

%e 1819677 is in the sequence as 1819677 = 1^6 + 1^6 + 3^6 + 3^6 + 6^6 + 11^6. (End)

%t Reap[For[n = 1, n <= 10000, n++, If[AnyTrue[PowersRepresentations[n, 6, 6], First[#] > 0&], Print[n]; Sow[n]]]][[2, 1]] (* _Jean-François Alcover_, Jul 18 2017 *)

%t With[{nn=5},Select[Total/@Tuples[Range[nn]^6,6]//Union,#<=nn^6-5&]] (* _Harvey P. Dale_, Mar 27 2022 *)

%Y Cf. A001014 (sixth powers).

%Y Column k=6 of A336725.

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_