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A368314 a(n) is the number of 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 A368314 #13 Dec 22 2023 11:39:47
%S A368314 1,2,2,3,3,4,3,4,4,5,5,6,5,6,5,5,5,7,6,7,7,8,7,8,7,8,8,9,7,10,7,6,7,7,
%T A368314 8,10,9,9,9,9,8,12,10,11,11,11,10,10,9,12,10,11,10,13,12,12,11,11,10,
%U A368314 15,11,13,11,7,8,11,9,9,10,13,10,13,11,12,14,12
%N A368314 a(n) is the number of 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 A368314 a(n) gives the number of terms in the n-th row of A368313.
%H A368314 Rémy Sigrist, <a href="/A368314/b368314.txt">Table of n, a(n) for n = 1..8192</a>
%H A368314 Rémy Sigrist, <a href="/A368314/a368314.gp.txt">PARI program</a>
%H A368314 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A368314 a(n) >= A000005(n).
%F A368314 a(2^k) = k + 1 for any k >= 0.
%e A368314 For n = 42: the 42nd row of A368313 contains 12 terms (1, 2, 3, 5, 6, 7, 10, 14, 21, 22, 26, 42), so a(42) = 12.
%o A368314 (PARI) See Links section.
%Y A368314 Cf. A000005, A368195 (decimal variant), A368313.
%K A368314 nonn,base
%O A368314 1,2
%A A368314 _Rémy Sigrist_, Dec 21 2023