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A173395 a(n) = (A002260(n) + 1) * (A004736(n) + 1).

%I A173395 #31 Oct 03 2024 06:30:41
%S A173395 4,6,6,8,9,8,10,12,12,10,12,15,16,15,12,14,18,20,20,18,14,16,21,24,25,
%T A173395 24,21,16,18,24,28,30,30,28,24,18,20,27,32,35,36,35,32,27,20,22,30,36,
%U A173395 40,42,42,40,36,30,22,24,33,40,45,48,49,48,45,40,33,24,26
%N A173395 a(n) = (A002260(n) + 1) * (A004736(n) + 1).
%C A173395 Every number of this sequence is composite, and every composite number appears in this sequence.
%C A173395 Viewed as a square array this sequence is the multiplication table with headers starting at 2: A002260 and A004736 being indexing functions for square arrays, a(n)=T(i,j) with i=A002260(n) and j=A004736(n), T(i,j)=(i+1)(j+1). - _Luc Rousseau_, Oct 15 2017
%H A173395 Michael De Vlieger, <a href="/A173395/b173395.txt">Table of n, a(n) for n = 1..11325</a> (rows 1 <= n <= 150).
%H A173395 Michael Somos, <a href="https://oeis.org/A073189/a073189.txt">Sequences used for indexing triangular or square arrays</a>.
%F A173395 a(n) = ((2 n + round(sqrt(2n)) - round(sqrt(2n))^2)/2 + 1)((2 - 2n + round(sqrt(2n)) + round(sqrt(2n))^2)/2 + 1).
%e A173395 4;
%e A173395 6,6;
%e A173395 8,9,8;
%e A173395 10,12,12,10;
%e A173395 12,15,16,15,12;
%e A173395 From _Luc Rousseau_, Oct 15 2017: (Start)
%e A173395 Viewed as a square array,
%e A173395    4  6  8 10 12 ...
%e A173395    6  9 12 15 18 ...
%e A173395    8 12 16 20 24 ...
%e A173395   10 15 20 25 30 ...
%e A173395   12 18 24 30 36 ...
%e A173395   ...
%e A173395 = the multiplication table with headers starting at 2.
%e A173395 (End)
%t A173395 Map[Times @@ # & /@ Transpose@{#, Reverse@ #} &, Array[Range, 12] + 1] // Flatten (* _Michael De Vlieger_, Oct 16 2017 *)
%o A173395 (PARI) a(n) = ((2*n + round(sqrt(2*n)) - round(sqrt(2*n))^2)/2 + 1)*((2 - 2*n + round(sqrt(2*n)) + round(sqrt(2*n))^2)/2 + 1) \\ _Michel Marcus_, Jun 19 2013
%o A173395 (PARI) a(n)=my(s=round(sqrt(n*=2)));(n-s-s^2-4)*(n+s-s^2+2)/4 \\ _Charles R Greathouse IV_, Jun 19 2013
%Y A173395 Cf. A002260, A004736.
%K A173395 nonn,easy,tabl
%O A173395 1,1
%A A173395 Fabio Civolani (civox(AT)tiscali.it), Feb 17 2010