A279667 - OEIS

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A279667

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

Individual edits:

#34 by Max Alekseyev at Thu Jul 16 08:51:20 EDT 2026

DATA

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, 48, 48

EXTENSIONS

STATUS

approved

All edits since published version (omitting small deletions for readability):

NAME

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

DATA

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, 48, 48

OFFSET

1,2

COMMENTS

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.

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

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

FORMULA

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

EXAMPLE

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.

CROSSREFS

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

KEYWORD

nonn,more

AUTHOR

Omar E. Pol, Dec 16 2016

EXTENSIONS

STATUS

approved