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Irregular triangle read by rows where row n lists all semiprimes whose prime indices sum to n.
27

%I #15 Dec 09 2020 12:06:39

%S 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 121,58,69,95,119,143,62,87,115,133,169,187,74,93,145,161,209,221,82,

%U 111,155,203,247,253,289,86,123,185,217,299,319,323,94,129,205

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

%C 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 Triangle begins:

%e 4

%e 6

%e 9 10

%e 14 15

%e 21 22 25

%e 26 33 35

%e 34 39 49 55

%e 38 51 65 77

%e 46 57 85 91 121

%e 58 69 95 119 143

%e 62 87 115 133 169 187

%e 74 93 145 161 209 221

%e 82 111 155 203 247 253 289

%e 86 123 185 217 299 319 323

%e 94 129 205 259 341 361 377 391

%t Table[Sort[Table[Prime[k]*Prime[n-k],{k,n/2}]],{n,2,10}]

%Y A004526 gives row lengths.

%Y A024697 gives row sums.

%Y A087112 is a different triangle of semiprimes.

%Y A098350 has antidiagonals with the same distinct terms as these rows.

%Y A338905 is the squarefree case, with row sums A025129.

%Y A338907/A338906 are the union of odd/even rows.

%Y A339114/A339115 are the row minima/maxima.

%Y A001358 lists semiprimes, with odd/even terms A046315/A100484.

%Y A006881 lists squarefree semiprimes, with odd/even terms A046388/A100484.

%Y A014342 is the self-convolution of primes.

%Y A037143 lists primes and semiprimes.

%Y A056239 gives sum of prime indices (Heinz weight).

%Y A062198 gives partial sums of semiprimes.

%Y A084126 and A084127 give the prime factors of semiprimes.

%Y A289182/A115392 list the positions of odd/even terms in A001358.

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

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

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

%Y Cf. A000040, A001221, A001222, A005117, A112798, A320732, A332877, A338908, A338910, A338911, A339116.

%K nonn,tabf

%O 2,1

%A _Gus Wiseman_, Nov 28 2020