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A090196 is a complement of this sequence in the set of odd numbers. - Hartmut F. W. Hoft, Dec 10 2016 [simplified by Omar E. Pol, Apr 17 2022]
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Let n = 2^m * q with m >= 0 and q odd. Let c_n denote the count of regions in the symmetric representation of sigma(n), which is determined by the positions of 1's in the n-th row of A237048. The maximum of c_n occurs when odd and even positions of 1's alternate implying that all regions have width 1, denoted by w_n = 1. When m > 0 then sigma_0(n) > sigma_0(q) and c_n = sigma_0(n) is impossible. Therefore, exactly those odd n with w_n = 1 are in this sequence. Furthermore, since the 1's in A237048 represent the odd divisors of n, their odd-even alternation expresses the property 2*f < g for any two adjacent divisors f < g of odd number n; in other words, this sequence is also the complement of A090196 relative to the odd numbers (see also A244969). This last property permits computations of elements in this sequence faster than with function a244579, which is based on Dyck paths. - Hartmut F. W. Hoft, Oct 11 2015
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A090196 is a complement of this sequence in the set of odd numbers. - Hartmut F. W. Hoft, Dec 10 2016 [simplified by Omar E. Pol, Apr 17 2022]
Since A244969 also A090196 is a complement of this sequence in the set of odd numbers this shows that A244969 = A090196. - Hartmut F. W. Hoft, Dec 10 2016 [simplified by _Omar E. Pol_, Apr 17 2022
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