A240062 -id:A240062 - cp's OEIS frontend

A320048 One half of composite numbers k with the property that the symmetric representation of sigma(k) has two parts.

5, 7, 11, 13, 17, 19, 22, 23, 26, 29, 31, 34, 37, 38, 39, 41, 43, 46, 47, 51, 53, 57, 58, 59, 61, 62, 67, 68, 69, 71, 73, 74, 76, 79, 82, 83, 86, 87, 89, 92, 93, 94, 97, 101, 103, 106, 107, 109, 111, 113, 116, 118, 122, 123, 124, 127, 129, 131, 134, 137, 139, 141, 142, 146, 148, 149, 151, 157, 158, 159, 163, 164

Offset: 1

Omar E. Pol, Oct 04 2018

nonn

Also, even numbers of A239929 divided by two.

First differs from A101550 at a(51). - R. J. Mathar, Oct 04 2018

			5 is in the sequence because 10 is a composite number, and the symmetric representation of sigma(10) = 18 has two parts (as shown below), and 10/2 = 5.
.
.     _ _ _ _ _ _ 9
.    |_ _ _ _ _  |
.              | |_
.              |_ _|_
.                  | |_ _ 9
.                  |_ _  |
.                      | |
.                      | |
.                      | |
.                      | |
.                      |_|
.

Cf. A101550, A237271 (number of parts), A237270, A237593, A238443, A238524, A239929 (two parts), A239660, A239929, A239932, A239934, A240062 (k parts), A244894, A245092, A262626, A280107 (four parts).

a(n) = A244894(n)/2.

A357775 Numbers k with the property that the symmetric representation of sigma(k) has seven parts.

Original entry on oeis.org

357, 399, 441, 483, 513, 567, 609, 621, 651, 729, 759, 777, 783, 837, 861, 891, 957, 999, 1023, 1053, 1089, 1107, 1131, 1161, 1209, 1221, 1269, 1287, 1323, 1353, 1419, 1431, 1443, 1521, 1551, 1595, 1599, 1677, 1705, 1749, 1815, 1833, 1887, 1947, 1989, 2013, 2035, 2067, 2091, 2145, 2193, 2223, 2255

Offset: 1

Omar E. Pol, Oct 12 2022

nonn

			357 is in the sequence because the 357th row of A237593 is [179, 60, 31, 18, 12, 9, 7, 6, 4, 4, 3, 3, 2, 3, 2, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 2, 3, 2, 3, 3, 4, 4, 6, 7, 9, 12, 18, 31, 60, 179], and the 356th row of the same triangle is [179, 60, 30, 18, 13, 9, 6, 6, 4, 4, 3, 3, 3, 2, 2, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 2, 2, 3, 3, 3, 4, 4, 6, 6, 9, 13, 18, 30, 60, 179], therefore between both symmetric Dyck paths there are seven parts: [179, 61, 29, 38, 29, 61, 179].
Note that the sum of these parts is 179 + 61 + 29 + 38 + 29 + 61 + 179 = 576, equaling the sum of the divisors of 357: 1 + 3 + 7 + 17 + 21 + 51 + 119 + 357 = 576.
(The diagram of the symmetric representation of sigma(357) = 576 is too large to include.)

Column 7 of A240062.
Cf. A237270 (the parts), A237271 (number of parts), A238443 = A174973 (one part), A239929 (two parts), A279102 (three parts), A280107 (four parts), A320066 (five parts), A320511 (six parts).
Cf. A018411, A196020, A236104, A235791, A237591, A237593, A239663, A266094.

A237271(a(n)) = 7.

cp's OEIS Frontend

A320048 One half of composite numbers k with the property that the symmetric representation of sigma(k) has two parts.

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