cp's OEIS Frontend

A338904 Irregular triangle read by rows where row n lists all semiprimes whose prime indices sum to n.

%I A338904 #15 Dec 09 2020 12:06:39
%S A338904 4,6,9,10,14,15,21,22,25,26,33,35,34,39,49,55,38,51,65,77,46,57,85,91,
%T A338904 121,58,69,95,119,143,62,87,115,133,169,187,74,93,145,161,209,221,82,
%U A338904 111,155,203,247,253,289,86,123,185,217,299,319,323,94,129,205
%N A338904 Irregular triangle read by rows where row n lists all semiprimes whose prime indices sum to n.
%C A338904 A semiprime is a product of any two 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 A338904 Triangle begins:
%e A338904    4
%e A338904    6
%e A338904    9  10
%e A338904   14  15
%e A338904   21  22  25
%e A338904   26  33  35
%e A338904   34  39  49  55
%e A338904   38  51  65  77
%e A338904   46  57  85  91 121
%e A338904   58  69  95 119 143
%e A338904   62  87 115 133 169 187
%e A338904   74  93 145 161 209 221
%e A338904   82 111 155 203 247 253 289
%e A338904   86 123 185 217 299 319 323
%e A338904   94 129 205 259 341 361 377 391
%t A338904 Table[Sort[Table[Prime[k]*Prime[n-k],{k,n/2}]],{n,2,10}]
%Y A338904 A004526 gives row lengths.
%Y A338904 A024697 gives row sums.
%Y A338904 A087112 is a different triangle of semiprimes.
%Y A338904 A098350 has antidiagonals with the same distinct terms as these rows.
%Y A338904 A338905 is the squarefree case, with row sums A025129.
%Y A338904 A338907/A338906 are the union of odd/even rows.
%Y A338904 A339114/A339115 are the row minima/maxima.
%Y A338904 A001358 lists semiprimes, with odd/even terms A046315/A100484.
%Y A338904 A006881 lists squarefree semiprimes, with odd/even terms A046388/A100484.
%Y A338904 A014342 is the self-convolution of primes.
%Y A338904 A037143 lists primes and semiprimes.
%Y A338904 A056239 gives sum of prime indices (Heinz weight).
%Y A338904 A062198 gives partial sums of semiprimes.
%Y A338904 A084126 and A084127 give the prime factors of semiprimes.
%Y A338904 A289182/A115392 list the positions of odd/even terms in A001358.
%Y A338904 A332765 gives the greatest squarefree semiprime of weight n.
%Y A338904 A338898, A338912, and A338913 give the prime indices of semiprimes, with product A087794, sum A176504, and difference A176506.
%Y A338904 A338899, A270650, and A270652 give the prime indices of squarefree semiprimes, with difference A338900.
%Y A338904 Cf. A000040, A001221, A001222, A005117, A112798, A320732, A332877, A338908, A338910, A338911, A339116.
%K A338904 nonn,tabf
%O A338904 2,1
%A A338904 _Gus Wiseman_, Nov 28 2020