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 A240061 Triangle read by rows, n>=1, 1<=k<=n. T(n,k) = number of cells in k-th row = number of cells in the k-th column of the diagram of the symmetric representation of sigma(n) in the first quadrant. 2
 1, 1, 2, 1, 1, 2, 1, 1, 2, 3, 1, 1, 1, 0, 3, 1, 1, 1, 3, 2, 4, 1, 1, 1, 1, 0, 0, 4, 1, 1, 1, 1, 3, 2, 1, 5, 1, 1, 1, 1, 1, 1, 2, 0, 5, 1, 1, 1, 1, 1, 3, 1, 2, 1, 6, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 6, 1, 1, 1, 1, 1, 1, 4, 3, 4, 3, 1, 7, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 7 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Since the diagram is symmetric the number of cells in the k-th row equals the number of cells in k-th column, see example. Row sums give A000203. Right border gives A008619, n >= 1. If n is an odd prime then row n lists (n+1)/2 ones, ((n+1)/2 - 2) zeros, and (n+1)/2. LINKS Table of n, a(n) for n=1..91. Index entries for sequences related to sigma(n) EXAMPLE Triangle begins: 1; 1, 2; 1, 1, 2; 1, 1, 2, 3; 1, 1, 1, 0, 3; 1, 1, 1, 3, 2, 4; 1, 1, 1, 1, 0, 0, 4; 1, 1, 1, 1, 3, 2, 1, 5; 1, 1, 1, 1, 1, 1, 2, 0, 5; 1, 1, 1, 1, 1, 3, 1, 2, 1, 6; 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 6; 1, 1, 1, 1, 1, 1, 4, 3, 4, 3, 1, 7; 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 7; ... For n = 9 the symmetric representation of sigma(9) = 13 in the first quadrant looks like this: y . Number of cells ._ _ _ _ _ |_ _ _ _ _| 5 . |_ _ 0 . |_ | 2 . |_|_ _ 1 . | | 1 . | | 1 . | | 1 . | | 1 . . . . . . . . |_| . . x 1 . So the 9th row of triangle is [1, 1, 1, 1, 1, 1, 2, 0, 5]. For n = 9 and k = 7 there are two cells in the 7th row of the diagram, also there are two cells in the 7th column of the diagram, so T(9,7) = 2. CROSSREFS Cf. A000203, A008619, A024916, A196020, A236104, A235791, A237270, A237271, A237591, A237593, A239660, A239931-A239934, A240060. Sequence in context: A029316 A104368 A218878 * A162320 A241911 A335221 Adjacent sequences: A240058 A240059 A240060 * A240062 A240063 A240064 KEYWORD nonn,tabl AUTHOR Omar E. Pol, Apr 26 2014 STATUS approved

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Last modified May 28 18:29 EDT 2023. Contains 363019 sequences. (Running on oeis4.)