cp's OEIS Frontend

A339116 Triangle of all squarefree semiprimes grouped by greater prime factor, read by rows.

%I A339116 #16 Feb 04 2024 22:01:00
%S A339116 6,10,15,14,21,35,22,33,55,77,26,39,65,91,143,34,51,85,119,187,221,38,
%T A339116 57,95,133,209,247,323,46,69,115,161,253,299,391,437,58,87,145,203,
%U A339116 319,377,493,551,667,62,93,155,217,341,403,527,589,713,899
%N A339116 Triangle of all squarefree semiprimes grouped by greater prime factor, read by rows.
%C A339116 A squarefree semiprime is a product of any two distinct prime numbers.
%H A339116 Andrew Howroyd, <a href="/A339116/b339116.txt">Table of n, a(n) for n = 2..1276</a> (first 50 rows)
%F A339116 T(n,k) = prime(n) * prime(k) for k < n.
%e A339116 Triangle begins:
%e A339116    6
%e A339116   10  15
%e A339116   14  21  35
%e A339116   22  33  55  77
%e A339116   26  39  65  91 143
%e A339116   34  51  85 119 187 221
%e A339116   38  57  95 133 209 247 323
%e A339116   46  69 115 161 253 299 391 437
%e A339116   58  87 145 203 319 377 493 551 667
%e A339116   62  93 155 217 341 403 527 589 713 899
%t A339116 Table[Prime[i]*Prime[j],{i,2,10},{j,i-1}]
%o A339116 (PARI) row(n) = {prime(n)*primes(n-1)}
%o A339116 { for(n=2, 10, print(row(n))) } \\ _Andrew Howroyd_, Jan 19 2023
%Y A339116 A339194 gives row sums.
%Y A339116 A100484 is column k = 1.
%Y A339116 A001748 is column k = 2.
%Y A339116 A001750 is column k = 3.
%Y A339116 A006094 is column k = n - 1.
%Y A339116 A090076 is column k = n - 2.
%Y A339116 A319613 is the central column k = 2*n.
%Y A339116 A087112 is the not necessarily squarefree version.
%Y A339116 A338905 is a different triangle of squarefree semiprimes.
%Y A339116 A339195 is the generalization to all squarefree numbers, row sums A339360.
%Y A339116 A001358 lists semiprimes.
%Y A339116 A005117 lists squarefree numbers.
%Y A339116 A006881 lists squarefree semiprimes, with odd terms A046388.
%Y A339116 A024697 is the sum of semiprimes of weight n.
%Y A339116 A025129 is the sum of squarefree semiprimes of weight n.
%Y A339116 A332765 gives the greatest squarefree semiprime of weight n.
%Y A339116 A338898/A338912/A338913 give the prime indices of semiprimes, with product A087794, sum A176504, and difference A176506.
%Y A339116 A338899/A270650/A270652 give the prime indices of squarefree semiprimes, with difference A338900.
%Y A339116 A338904 groups semiprimes by weight.
%Y A339116 A338907/A338908 list squarefree semiprimes of odd/even weight.
%Y A339116 Cf. A000040, A001221, A014342, A098350, A112798, A168472, A320656, A338901, A339003, A339114/A339115.
%Y A339116 Subsequence of A019565.
%K A339116 nonn,easy,tabl
%O A339116 2,1
%A A339116 _Gus Wiseman_, Dec 01 2020
%E A339116 Offset corrected by _Andrew Howroyd_, Jan 19 2023