OFFSET
1,2
COMMENTS
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..416 (terms < 10^9)
FORMULA
EXAMPLE
gcd(1,24)=1 and 1*(1+24)*(1+2*24) = 25*49 = (5*7)^2, so 5*7 = 35 is a member.
gcd(18,7)=1 and 18*(18+7)*(18+2*7) = 18*25*32 = 9*25*64 = (3*5*8)^2, so 3*5*8 = 120 is in the sequence.
MATHEMATICA
nn = 50000; t = {};
p[a_, b_, c_] := a b c; Do[
If[p[a, a + d, a + 2 d] <= 2 nn^2 && GCD[a, d] == 1 &&
IntegerQ[Sqrt[p[a, a + d, a + 2 d]]],
AppendTo[t, Sqrt[p[a, a + d, a + 2 d]]]], {a, 1, nn}, {d, 0, nn}]; Sort[t]
PROG
(PARI) is(n, s)={!fordiv(n*=n, a, a^3>n && return; issquare(n\a*8+a^2, &s) && (s-=3*a)%4==0 && gcd(s\4, a)==1 && break)} \\ M. F. Hasler, Apr 06 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Jonathan Sondow, Apr 05 2017
EXTENSIONS
a(19)-a(37) from Giovanni Resta, Apr 06 2017
STATUS
approved