A339410 If the n-th semiprime is p*q with p<=q primes, a(n) is the area of the triangle with vertices (1,p), (p,q) and (q,p*q).

1, 1, 6, 2, 9, 8, 6, 35, 40, 54, 10, 104, 54, 135, 24, 209, 126, 64, 70, 90, 350, 405, 72, 154, 594, 190, 740, 64, 819, 280, 216, 330, 989, 54, 1274, 504, 22, 1595, 256, 550, 1710, 640, 714, 270, 2079, 874, 2345, 648, 56, 2484, 90, 2925, 1144, 286, 3239, 936, 1450, 3740, 1560, 216, 832, 4464

Offset: 1

Author

J. M. Bergot and Robert Israel, Dec 03 2020

Keywords

• nonn
• look

Examples

			For n = 5 the 5th semiprime is 14=2*7, and the area of the triangle with vertices (1,2), (2,7) and (7,14) is a(5)=9.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001358, A084126, A084127.

Programs

Maple

N:= 1000: # for semiprimes <= N
SP:= select(t -> numtheory:-bigomega(t)=2, [$4..N]):
f:= proc(n) local p,q;
  p,q:= (min,max)(numtheory:-factorset(n));
  (q-1)*abs(p^2-q)/2
end proc:
map(f, SP);

Mathematica

ar[{a_,b_}]:=Abs[Det[{{1,a,b},{a,b,a b},{1,1,1}}]]/2; ar/@(If[Length[#]==1,Flatten[ {#,#}],#]&/@(FactorInteger[#][[;;,1]]&/@Select[Range[200],PrimeOmega[ #] == 2&])) (* Harvey P. Dale, Mar 05 2023 *)

Formula

a(n) = (q-1)*|p^2-q|/2 where p = A084126(n) and q = A084127(n).