A236711 - OEIS

%I #27 Jul 07 2015 07:26:13

%S 5281250,9031250,21125000,26281250,36125000,42781250,47531250,

%T 52531250,81281250,84500000,87781250,105125000,116281250,126953125,

%U 144500000,166015625,166531250,171125000,190125000,210125000,236531250,241340450,247531250,253906250,258781250

%N Numbers that are the sum of 2 nonzero squares in exactly 11 ways.

%C Are all terms multiples of 5?

%C The answer is "no"; 2789895602 = 2 * 13^6 * 17^2 is a term that is not a multiple of 5. Is it the first such term? - _Zak Seidov_, Jul 05 2015

%C a(152) = 2789895602 is the first term that is not divisible by 5. In the first 1000 terms, the only powers to which 5 appears as a factor are 0 (for 10 terms, beginning with a(152), after which the next does not occur until a(331)), 2 (for only 14 terms, the smallest of which is a(22) = 241340450 = 2 * 5^2 * 13^6), 6 (for 360 terms), and 10 (for the remaining 616 terms). - _Jon E. Schoenfield_, Jul 07 2015

%H Jon E. Schoenfield, <a href="/A236711/b236711.txt">Table of n, a(n) for n = 1..1000</a>

%H C. Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_062.htm">Puzzle 62</a>

%e 5281250 = x^2 + y^2 with {x,y} = {71,2297}, {245,2285}, {325,2275}, {575,2225}, {875,2125}, {949,2093}, {1105,2015}, {1175,1975}, {1435,1795}, {1567,1681}, {1625,1625}.

%Y Cf.  A000404, A016032, A025285-A025293.

%K nonn

%O 1,1

%A _Zak Seidov_, Jan 30 2014

%E More terms from _Jon E. Schoenfield_, Jul 05 2015