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A357775
Numbers k with the property that the symmetric representation of sigma(k) has seven parts.
1
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
1,1
FORMULA
A237271(a(n)) = 7.
EXAMPLE
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.)
CROSSREFS
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).
Sequence in context: A232851 A223428 A277765 * A052479 A252806 A252027
KEYWORD
nonn
AUTHOR
Omar E. Pol, Oct 12 2022
STATUS
approved