A339116 - OEIS

%I #16 Feb 04 2024 22:01:00

%S 6,10,15,14,21,35,22,33,55,77,26,39,65,91,143,34,51,85,119,187,221,38,

%T 57,95,133,209,247,323,46,69,115,161,253,299,391,437,58,87,145,203,

%U 319,377,493,551,667,62,93,155,217,341,403,527,589,713,899

%N Triangle of all squarefree semiprimes grouped by greater prime factor, read by rows.

%C A squarefree semiprime is a product of any two distinct prime numbers.

%H Andrew Howroyd, <a href="/A339116/b339116.txt">Table of n, a(n) for n = 2..1276</a> (first 50 rows)

%F T(n,k) = prime(n) * prime(k) for k < n.

%e Triangle begins:

%e    6

%e   10  15

%e   14  21  35

%e   22  33  55  77

%e   26  39  65  91 143

%e   34  51  85 119 187 221

%e   38  57  95 133 209 247 323

%e   46  69 115 161 253 299 391 437

%e   58  87 145 203 319 377 493 551 667

%e   62  93 155 217 341 403 527 589 713 899

%t Table[Prime[i]*Prime[j],{i,2,10},{j,i-1}]

%o (PARI) row(n) = {prime(n)*primes(n-1)}

%o { for(n=2, 10, print(row(n))) } \\ _Andrew Howroyd_, Jan 19 2023

%Y A339194 gives row sums.

%Y A100484 is column k = 1.

%Y A001748 is column k = 2.

%Y A001750 is column k = 3.

%Y A006094 is column k = n - 1.

%Y A090076 is column k = n - 2.

%Y A319613 is the central column k = 2*n.

%Y A087112 is the not necessarily squarefree version.

%Y A338905 is a different triangle of squarefree semiprimes.

%Y A339195 is the generalization to all squarefree numbers, row sums A339360.

%Y A001358 lists semiprimes.

%Y A005117 lists squarefree numbers.

%Y A006881 lists squarefree semiprimes, with odd terms A046388.

%Y A024697 is the sum of semiprimes of weight n.

%Y A025129 is the sum of squarefree semiprimes of weight n.

%Y A332765 gives the greatest squarefree semiprime of weight n.

%Y A338898/A338912/A338913 give the prime indices of semiprimes, with product A087794, sum A176504, and difference A176506.

%Y A338899/A270650/A270652 give the prime indices of squarefree semiprimes, with difference A338900.

%Y A338904 groups semiprimes by weight.

%Y A338907/A338908 list squarefree semiprimes of odd/even weight.

%Y Cf. A000040, A001221, A014342, A098350, A112798, A168472, A320656, A338901, A339003, A339114/A339115.

%Y Subsequence of A019565.

%K nonn,easy,tabl

%O 2,1

%A _Gus Wiseman_, Dec 01 2020

%E Offset corrected by _Andrew Howroyd_, Jan 19 2023