cp's OEIS Frontend

A338905 Irregular triangle read by rows where row n lists all squarefree semiprimes with prime indices summing to n.

%I A338905 #12 Dec 06 2020 06:28:18
%S A338905 6,10,14,15,21,22,26,33,35,34,39,55,38,51,65,77,46,57,85,91,58,69,95,
%T A338905 119,143,62,87,115,133,187,74,93,145,161,209,221,82,111,155,203,247,
%U A338905 253,86,123,185,217,299,319,323,94,129,205,259,341,377,391,106,141
%N A338905 Irregular triangle read by rows where row n lists all squarefree semiprimes with prime indices summing to n.
%C A338905 A squarefree semiprime is a product of any two distinct prime numbers. A prime index of n is a number m such that the m-th prime number divides n. The multiset of prime indices of n is row n of A112798.
%e A338905 Triangle begins:
%e A338905    6
%e A338905   10
%e A338905   14  15
%e A338905   21  22
%e A338905   26  33  35
%e A338905   34  39  55
%e A338905   38  51  65  77
%e A338905   46  57  85  91
%e A338905   58  69  95 119 143
%e A338905   62  87 115 133 187
%e A338905   74  93 145 161 209 221
%e A338905   82 111 155 203 247 253
%e A338905   86 123 185 217 299 319 323
%t A338905 Table[Sort[Table[Prime[k]*Prime[n-k],{k,(n-1)/2}]],{n,3,10}]
%Y A338905 A004526 (shifted right) gives row lengths.
%Y A338905 A025129 (shifted right) gives row sums.
%Y A338905 A056239 gives sum of prime indices (Heinz weight).
%Y A338905 A339116 is a different triangle whose diagonals are these rows.
%Y A338905 A338904 is the not necessarily squarefree version, with row sums A024697.
%Y A338905 A338907/A338908 are the union of odd/even rows.
%Y A338905 A339114/A332765 are the row minima/maxima.
%Y A338905 A001358 lists semiprimes, with odd/even terms A046315/A100484.
%Y A338905 A005117 lists squarefree numbers.
%Y A338905 A006881 lists squarefree semiprimes, with odd/even terms A046388/A100484.
%Y A338905 A087112 groups semiprimes by greater factor.
%Y A338905 A168472 gives partial sums of squarefree semiprimes.
%Y A338905 A338898, A338912, and A338913 give the prime indices of semiprimes, with product A087794, sum A176504, and difference A176506.
%Y A338905 A338899, A270650, and A270652 give the prime indices of squarefree semiprimes, with difference A338900.
%Y A338905 Cf. A000040, A001221, A014342, A098350, A112798, A320656, A338901, A338906, A339003, A339004, A339005, A339115.
%K A338905 nonn,tabf
%O A338905 3,1
%A A338905 _Gus Wiseman_, Nov 28 2020