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Irregular triangle read by rows in which row n lists numbers d-1 that do not divide n, where d divides n.
3

%I #24 Apr 02 2017 00:46:50

%S 2,3,4,5,6,3,7,2,8,4,9,10,5,11,12,6,13,2,4,14,3,7,15,16,5,8,17,18,3,9,

%T 19,2,6,20,10,21,22,5,7,11,23,4,24,12,25,2,8,26,3,6,13,27,28,4,9,14,

%U 29,30,3,7,15,31,2,10,32,16,33,4,6,34,5,8,11,17,35

%N Irregular triangle read by rows in which row n lists numbers d-1 that do not divide n, where d divides n.

%C It appears that only rows 3, 4, 6, 8, 12, 24 have the property that all their members are primes. See the example. See also the comment at A018253.

%H T. D. Noe, <a href="/A195153/b195153.txt">Rows n = 3..1000, flattened</a>

%e Written as an irregular triangle:

%e 2,

%e 3,

%e 4,

%e 5,

%e 6,

%e 3, 7,

%e 2, 8,

%e 4, 9,

%e 10,

%e 5, 11,

%e 12,

%e 6, 13,

%e 2, 4, 14,

%e 3, 7, 15,

%e 16,

%e 5, 8, 17,

%e 18,

%e 3, 9, 19,

%e 2, 6, 20,

%e 10, 21,

%e 22,

%e 5, 7, 11, 23

%t Flatten[Table[d = Divisors[n]; Select[Rest[d-1], Mod[n, #] > 0 &], {n, 3 , 100}]] (* _T. D. Noe_, Sep 23 2011 *)

%Y Cf. A018253, A027750, A173540, A195150.

%K nonn,tabf

%O 3,1

%A _Omar E. Pol_, Sep 19 2011