cp's OEIS Frontend

A367096 Irregular triangle read by rows where row n lists the semiprime divisors of n. Alternatively, row n lists the semiprime divisors of A002808(n).

%I A367096 #9 May 02 2025 03:31:39
%S A367096 4,6,4,9,10,4,6,14,15,4,6,9,4,10,21,22,4,6,25,26,9,4,14,6,10,15,4,33,
%T A367096 34,35,4,6,9,38,39,4,10,6,14,21,4,22,9,15,46,4,6,49,10,25,51,4,26,6,9,
%U A367096 55,4,14,57,58,4,6,10,15,62,9,21,4,65,6,22,33,4,34
%N A367096 Irregular triangle read by rows where row n lists the semiprime divisors of n. Alternatively, row n lists the semiprime divisors of A002808(n).
%C A367096 On the first interpretation, the first three rows are empty. On the second, the first row is (4).
%e A367096 The semiprime divisors of 30 are {6,10,15}, so row 30 is (6,10,15). Without empty rows, this is row 19.
%e A367096 Triangle begins (empty rows indicated by dots):
%e A367096    1: .
%e A367096    2: .
%e A367096    3: .
%e A367096    4: 4
%e A367096    5: .
%e A367096    6: 6
%e A367096    7: .
%e A367096    8: 4
%e A367096    9: 9
%e A367096   10: 10
%e A367096   11: .
%e A367096   12: 4,6
%e A367096 Without empty rows:
%e A367096    1: 4
%e A367096    2: 6
%e A367096    3: 4
%e A367096    4: 9
%e A367096    5: 10
%e A367096    6: 4,6
%e A367096    7: 14
%e A367096    8: 15
%e A367096    9: 4
%e A367096   10: 6,9
%e A367096   11: 4,10
%e A367096   12: 21
%t A367096 Table[Select[Divisors[n],PrimeOmega[#]==2&],{n,100}]
%o A367096 (PARI) row(n) = select(x -> bigomega(x) == 2, divisors(n)); \\ _Amiram Eldar_, May 02 2025
%Y A367096 For all divisors we have A027750.
%Y A367096 Square terms are counted by A056170.
%Y A367096 Row sums are A076290.
%Y A367096 Squarefree terms are counted by A079275.
%Y A367096 Row lengths are A086971, firsts A220264.
%Y A367096 A000005 counts divisors.
%Y A367096 A001222 counts prime factors (or prime indices), distinct A001221.
%Y A367096 A001358 lists semiprimes, squarefree A006881, complement A100959.
%Y A367096 Cf. A008967, A365829, A366738, A366739, A366740, A367093, A367098.
%K A367096 nonn,tabf
%O A367096 1,1
%A A367096 _Gus Wiseman_, Nov 08 2023