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A163870 Triangle read by rows: row n lists the nontrivial divisors of the n-th composite.

%I A163870 #18 Dec 26 2024 15:21:05
%S A163870 2,2,3,2,4,3,2,5,2,3,4,6,2,7,3,5,2,4,8,2,3,6,9,2,4,5,10,3,7,2,11,2,3,
%T A163870 4,6,8,12,5,2,13,3,9,2,4,7,14,2,3,5,6,10,15,2,4,8,16,3,11,2,17,5,7,2,
%U A163870 3,4,6,9,12,18,2,19,3,13,2,4,5,8,10,20,2,3,6,7,14,21,2,4,11,22,3,5,9,15,2,23
%N A163870 Triangle read by rows: row n lists the nontrivial divisors of the n-th composite.
%C A163870 Row n contains row A002808(n) of table A027750.
%C A163870 T(n,k) = A027751(A002808(n),k+1), k = 1..A144925(n). - _Reinhard Zumkeller_, Mar 29 2014
%H A163870 Reinhard Zumkeller, <a href="/A163870/b163870.txt">Rows n = 1..1000 of table, flattened</a>
%e A163870 The table starts in row n=1 (with the composite 4) as
%e A163870   2;
%e A163870   2,3;
%e A163870   2,4;
%e A163870   3;
%e A163870   2,5;
%e A163870   2,3,4,6;
%e A163870   2,7;
%e A163870   3,5;
%e A163870   2,4,8;
%e A163870   2,3,6,9;
%e A163870   2,4,5,10.
%t A163870 Divisors[Select[Range[50], CompositeQ]][[All, 2 ;; -2]] (* _Paolo Xausa_, Dec 26 2024 *)
%o A163870 (Haskell)
%o A163870 a163870 n k = a163870_tabf !! (n-1) !! (k-1)
%o A163870 a163870_row n = a163870_tabf !! (n-1)
%o A163870 a163870_tabf = filter (not . null) $ map tail a027751_tabf
%o A163870 -- _Reinhard Zumkeller_, Mar 29 2014
%o A163870 (Python)
%o A163870 from itertools import islice
%o A163870 def g():
%o A163870     n, j = 1, 2
%o A163870     while True:
%o A163870         n = (n << 1) | 1
%o A163870         p = 1
%o A163870         for k in range(2, (j >> 1) + 1):
%o A163870             p = (p << 1) | 1
%o A163870             if n % p == 0: yield k
%o A163870         j+=1
%o A163870 print(list(islice(g(),95))) # _Darío Clavijo_, Dec 16 2024
%Y A163870 Cf. A002808, A027750.
%Y A163870 Cf. A144925 (row lengths), A062825 (row sums), A056608 (left edge), A160180 (right edge).
%K A163870 nonn,tabf
%O A163870 1,1
%A A163870 _Juri-Stepan Gerasimov_, Aug 06 2009
%E A163870 Entries checked by _R. J. Mathar_, Sep 22 2009