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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A235334 Numbers n such that for any positive integers (a, b), if a * b = n then a + b is a square.

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%I A235334 #18 Oct 02 2014 07:51:14
%S A235334 3,323,5183,777923,1327103,6718463,12446783,16402499,229159043,
%T A235334 432972863,1214383103,2191925123,4787532863,6927565823,10809345023,
%U A235334 12619826243,22218287363,31123310723,32399999999,42469790723,79101562499,131734154303,151291437443
%N A235334 Numbers n such that for any positive integers (a, b), if a * b = n then a + b is a square.
%C A235334 It seems that n is the product of twin primes of A232878 for n > 3.
%C A235334 Conjecture: the numbers n such that for any positive integers (a, b), a * b = n and a + b is a square are the product of twin primes, and a*b+1 is also a perfect square.
%H A235334 Hiroaki Yamanouchi, <a href="/A235334/b235334.txt">Table of n, a(n) for n = 1..1163</a>
%e A235334 323 is the product of two positive integers in 2 ways: 1 * 323 and 17 * 19. The sums of the pairs of multiplicands are 323+1 = 18^2 and 17+19 = 6^2 respectively. All are squares.
%t A235334 t={}; Do[ds=Divisors[n]; If[EvenQ[Length[ds]], ok=True; k=1; While[k<=Length[ds]/2 && (ok=IntegerQ[Sqrt[ds[[k]]+ds[[ -k]]]]), k++ ]; If[ok, AppendTo[t, n]]], {n, 2, 10^8}]; t ***[Program from T.D. Noe adapted for this sequence. See A080715]***
%o A235334 (PARI) isok(n) = {d = divisors(n); if (#d % 2, return (0)); for (i = 1, #d/2, if (! issquare(d[i]+n/d[i]), return (0));); return (1);} \\ _Michel Marcus_, Jan 06 2014
%Y A235334 Cf. A001097, A080715, A232878.
%K A235334 nonn
%O A235334 1,1
%A A235334 _Michel Lagneau_, Jan 06 2014
%E A235334 a(21)-a(23) from _Hiroaki Yamanouchi_, Oct 02 2014