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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. 4

%I #13 Dec 22 2023 11:39:47

%S 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 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 15,11,13,11,7,8,11,9,9,10,13,10,13,11,12,14,12

%N 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 a(n) gives the number of terms in the n-th row of A368313.

%H Rémy Sigrist, <a href="/A368314/b368314.txt">Table of n, a(n) for n = 1..8192</a>

%H Rémy Sigrist, <a href="/A368314/a368314.gp.txt">PARI program</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%F a(n) >= A000005(n).

%F a(2^k) = k + 1 for any k >= 0.

%e 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 (PARI) See Links section.

%Y Cf. A000005, A368195 (decimal variant), A368313.

%K nonn,base

%O 1,2

%A _Rémy Sigrist_, Dec 21 2023

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Last modified September 6 10:06 EDT 2024. Contains 375712 sequences. (Running on oeis4.)