A245810 - OEIS

%I #38 Sep 12 2020 10:30:56

%S 0,1,3,4,6,9,10,15,16,19,21,25,28,31,33,36,45,46,49,51,55,64,66,73,76,

%T 78,81,85,91,99,100,105,106,109,120,121,129,136,141,144,145,153,163,

%U 166,169,171,181,190,196,199,201,210,225,226,231,235,241,243

%N Genus of the complete intersection of two hypersurfaces in P^3.

%C Integers that can be written as d*e*(d+e-4)/2+1 for positive integers d and e.

%H Jean-François Alcover, <a href="/A245810/b245810.txt">Table of n, a(n) for n = 1..10000</a>

%p filter:= proc(n)

%p local m,S,Q;

%p m:= 2*(n-1);

%p S:= numtheory:-divisors(m);

%p Q:= map(d ->(4*d-m+sqrt(4*d^3 + 16*d^2 - 8*d*m + m^2))/(2*d), S);

%p evalb(select(type,Q,posint) <> {})

%p end proc:

%p filter(0):= true:

%p filter(1):= true:

%p select(filter, [$0..1000]); # _Robert Israel_, Aug 24 2014

%t Module[{gmax = 300, g}, Reap[Do[g = d e (d + e - 4)/2 + 1; If[IntegerQ[g], Sow[g]], {d, Ceiling[(3 + Sqrt[1 + 8 gmax])/2]}, {e, d}]][[2, 1]] // Select[#, # <= gmax &]& // Union] (* _Jean-François Alcover_, Sep 12 2020 *)

%K nonn

%O 1,3

%A _Richard Shadrach_, Aug 22 2014

%E b-file corrected by _Jean-François Alcover_, Sep 12 2020