OFFSET
1,4
COMMENTS
This is a 2-column table read by rows. For each row a,d the product a*(a+d)*(a+2*d) is a square. The rows are ordered by those products.
The main entry for this sequence is A284666, formed by the triples a, a+d, a+2*d. The square roots of the products a*(a+d)*(a+2*d) form A284876.
For a=1 the d values 0, 24, 840, 28560, ... are A078522.
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..832
FORMULA
EXAMPLE
gcd(18,7)=1 and 18*(18+7)*(18+2*7) = 18*25*32 = 9*25*64 = (3*5*8)^2, so 18,7 is in the sequence.
MATHEMATICA
nn = 50000; t = {};
p[a_, d_] := a (a + d) (a + 2 d); Do[
If[p[a, d] <= 2 nn^2 && GCD[a, d] == 1 && IntegerQ[Sqrt[p[a, d]]],
AppendTo[t, {a, d}]], {a, 1, nn}, {d, 0, nn}];
Sort[t, p[#1[[1]], #1[[2]]] < p[#2[[1]], #2[[2]]] &] // Flatten
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Jonathan Sondow, Apr 04 2017
EXTENSIONS
a(37)-a(52) from Giovanni Resta, Apr 06 2017
STATUS
approved