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Number of subparts (also number of odd divisors) of the smallest number k such that the symmetric representation of sigma(k) has n layers.
2

%I #33 Jan 11 2017 03:25:42

%S 1,2,4,4,6,8,8,12,12,12,16,24,24,18,32,32,24,36,24,36,32,48,36,32,48,

%T 48,48

%N Number of subparts (also number of odd divisors) of the smallest number k such that the symmetric representation of sigma(k) has n layers.

%C In other words: number of subparts (also number of odd divisors) of the smallest number k such that the symmetric representation of sigma(k) has at least a part of width n.

%C Note that the number of subparts in the symmetric representation of sigma(n) equals A001227(n), the number of odd divisors of n.

%C For more information about the subparts and the layers see A279387.

%F a(n) = A001227(A250070(n)).

%e For n = 5 we have that 360 is the smallest number k whose symmetric representation of sigma(k) has parts of width 5. The structure has six subparts: [719, 237, 139, 71, 2, 2]. On the other hand, 360 has six odd divisors: {1, 3, 5, 9, 15, 45}, so a(5) = 6.

%Y Cf. A000203, A001227, A005279, A196020, A236104, A235791, A237048, A237270, A237271, A237591, A237593, A239657, A244050, A245092, A250070, A261699, A279387, A279388, A279391.

%K nonn,more

%O 1,2

%A _Omar E. Pol_, Dec 16 2016