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A320521 a(n) is the smallest even number k such that the symmetric representation of sigma(k) has n parts. 1
2, 10, 50, 230, 1150 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(6) > 5001.

LINKS

Table of n, a(n) for n=1..5.

EXAMPLE

a(1) = 2 because the second row of A237593 is [2, 2], and the first row of the same triangle is [1, 1], therefore between both symmetric Dyck paths there is only one part: [3], equaling the sum of the divisors of 2: 1 + 2 = 3. See below:

.

.     _ _ 3

.    |_  |

.      |_|

.

.

a(2) = 10 because the 10th row of A237593 is [6, 2, 1, 1, 1, 1, 2, 6], and the 9th row of the same triangle is [5, 2, 2, 2, 2, 5], therefore between both symmetric Dyck paths there are two parts: [9, 9]. Also there are no even numbers k < 10 whose symmetric representation of sigma(k) has two parts. Note that the sum of these parts is 9 + 9 = 18, equaling the sum of the divisors of 10: 1 + 2 + 5 + 10 = 18. See below:

.

.     _ _ _ _ _ _ 9

.    |_ _ _ _ _  |

.              | |_

.              |_ _|_

.                  | |_ _ 9

.                  |_ _  |

.                      | |

.                      | |

.                      | |

.                      | |

.                      |_|

.

a(3) = 50 because the 50th row of A237593 is [26, 9, 4, 3, 3, 1, 2, 1, 1, 1, 1, 2, 1, 3, 3, 4, 9, 26], and the 49th row of the same triangle is [25, 9, 5, 3, 2, 1, 2, 1, 1, 1, 1, 2, 1, 2, 3, 5, 9, 25], therefore between both symmetric Dyck paths there are three parts: [39, 15, 39]. Also there are no even numbers k < 50 whose symmetric representation of sigma(k) has three parts. Note that the sum of these parts is 39 + 15 + 39 = 93, equaling the sum of the divisors of 50: 1 + 2 + 5 + 10 + 25 + 50 = 93. (The diagram of the symmetric representation of sigma(50) = 93 is too large to include.)

CROSSREFS

Row 1 of A320537.

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. A000203, A018262, A005843, A196020, A235791, A236104, A237048, A237591, A237593, A239663, A239665, A240062, A245092, A262626, A296508.

Sequence in context: A317111 A337348 A218778 * A180266 A015945 A015954

Adjacent sequences:  A320518 A320519 A320520 * A320522 A320523 A320524

KEYWORD

nonn,more,hard

AUTHOR

Omar E. Pol, Oct 14 2018

STATUS

approved

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Last modified April 15 01:24 EDT 2021. Contains 342974 sequences. (Running on oeis4.)