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A368313 Irregular table T(n, k), n > 0, k = 1..A368314(n), read by rows: the n-th row lists the numbers that can be obtained by replacing any positive number without leading zeros, say m, appearing in the binary expansion of n by one of the divisors of m.

%I A368313 #11 Dec 22 2023 11:39:39
%S A368313 1,1,2,1,3,1,2,4,1,3,5,1,2,3,6,1,3,7,1,2,4,8,1,3,5,9,1,2,5,6,10,1,3,5,
%T A368313 7,11,1,2,3,4,6,12,1,3,5,7,13,1,2,3,6,7,14,1,3,5,7,15,1,2,4,8,16,1,3,
%U A368313 5,9,17,1,2,3,6,9,10,18,1,3,7,9,11,19,1,2,4,5,10,12,20
%N A368313 Irregular table T(n, k), n > 0, k = 1..A368314(n), read by rows: the n-th row lists the numbers that can be obtained by replacing any positive number without leading zeros, say m, appearing in the binary expansion of n by one of the divisors of m.
%C A368313 The n-th row starts with 1, ends with n, and contains the divisors of n (A027750).
%H A368313 Rémy Sigrist, <a href="/A368313/b368313.txt">Table of n, a(n) for n = 1..10177</a> (rows for n = 1..2^9 flattened)
%H A368313 Rémy Sigrist, <a href="/A368313/a368313.gp.txt">PARI program</a>
%H A368313 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A368313 T(n, 1) = 1.
%F A368313 T(n, A368314(n)) = n.
%e A368313 Table T(n, k) begins:
%e A368313     1;
%e A368313     1, 2;
%e A368313     1, 3;
%e A368313     1, 2, 4;
%e A368313     1, 3, 5;
%e A368313     1, 2, 3, 6;
%e A368313     1, 3, 7;
%e A368313     1, 2, 4, 8;
%e A368313     1, 3, 5, 9;
%e A368313     1, 2, 5, 6, 10;
%e A368313     1, 3, 5, 7, 11;
%e A368313     1, 2, 3, 4, 6, 12;
%e A368313     1, 3, 5, 7, 13;
%e A368313     1, 2, 3, 6, 7, 14;
%e A368313     1, 3, 5, 7, 15;
%e A368313     1, 2, 4, 8, 16;
%e A368313     1, 3, 5, 9, 17;
%e A368313     ...
%o A368313 (PARI) See Links section.
%Y A368313 Cf. A027750, A368194 (decimal variant), A368314.
%K A368313 nonn,base,tabf
%O A368313 1,3
%A A368313 _Rémy Sigrist_, Dec 21 2023