cp's OEIS Frontend

A379374 Irregular triangle read by rows in which row n lists the divisors of n except the divisors "e" described in A005279.

%I A379374 #67 Jan 25 2025 12:34:57
%S A379374 1,1,2,1,3,1,2,4,1,5,1,2,6,1,7,1,2,4,8,1,3,9,1,2,5,10,1,11,1,2,12,1,
%T A379374 13,1,2,7,14,1,3,15,1,2,4,8,16,1,17,1,2,6,18,1,19,1,2,4,10,20,1,3,7,
%U A379374 21,1,2,11,22,1,23,1,2,24,1,5,25,1,2,13,26,1,3,9,27
%N A379374 Irregular triangle read by rows in which row n lists the divisors of n except the divisors "e" described in A005279.
%C A379374 Observation: the sequence of the number of odd terms in row n coincides with at least the first 10000 terms of A237271.
%C A379374 The observation is true for all numbers. For a proof see A379288. - _Hartmut F. W. Hoft_, Jan 25 2025
%e A379374 Triangle begins:
%e A379374   1;
%e A379374   1,  2;
%e A379374   1,  3;
%e A379374   1,  2,  4;
%e A379374   1,  5;
%e A379374   1,  2,  6;
%e A379374   1,  7;
%e A379374   1,  2,  4,  8;
%e A379374   1,  3,  9;
%e A379374   1,  2,  5, 10;
%e A379374   1, 11;
%e A379374   1,  2, 12;
%e A379374   1, 13;
%e A379374   1,  2,  7, 14;
%e A379374   1,  3, 15;
%e A379374   1,  2,  4,  8, 16;
%e A379374   1, 17;
%e A379374   1,  2,  6, 18;
%e A379374   1, 19;
%e A379374   1,  2,  4, 10, 20;
%e A379374   ...
%t A379374 row[n_] := Module[{d = Partition[Divisors[n], 2, 1]}, Join[{1}, Select[d, #[[2]] >= 2*#[[1]] &][[;; , 2]]]]; Table[row[n], {n, 1, 27}] // Flatten (* _Amiram Eldar_, Dec 22 2024 *)
%Y A379374 Subsequence of A027750.
%Y A379374 Row sums give A379384.
%Y A379374 Odd terms give A379288.
%Y A379374 Cf. A001227, A005279, A010814, A237271, A237593, A239657, A237271, A379379.
%K A379374 nonn,tabf
%O A379374 1,3
%A A379374 _Omar E. Pol_, Dec 21 2024
%E A379374 More terms from _Alois P. Heinz_, Dec 21 2024