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 A130540 Triangle read by rows T(n,k) in which column k lists the terms of A000203 interspersed with (k-1) zeros, 1 <= k <= n. 2
 1, 3, 1, 4, 0, 1, 7, 3, 0, 1, 6, 0, 0, 0, 1, 12, 4, 3, 0, 0, 1, 8, 0, 0, 0, 0, 0, 1, 15, 7, 0, 3, 0, 0, 0, 1, 13, 0, 4, 0, 0, 0, 0, 0, 1, 18, 6, 0, 0, 3, 0, 0, 0, 0, 1, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 28, 12, 7, 4, 0, 3, 0, 0, 0, 0, 0, 1, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 24, 8, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The original definition was: A127093 * A125093^(-1). Left border = A000203, sigma(n): (1, 3, 4, 7, 6, ...). Row sums = A007429: (1, 4, 5, 11, 7, 20, 9, ...); = inverse Moebius transform applied to sigma(n); (i.e., inverse Moebius transform applied twice to natural numbers). T(n,k) is the total number of parts congruent to 0 mod k in the partitions of n into equal parts. - Omar E. Pol, Nov 19 2019 From Omar E. Pol, Jan 01 2020: (Start) Conjecture 1: the sum of odd-indexed terms in row n equals A327096(n). Conjecture 2: the sum of even-indexed terms in row n equals the n-th term of the sequence formed by A000004 and A007429 interleaved. Conjecture 3: alternating row sums give A288417. (End) LINKS FORMULA A127093 * A125093^(-1), as infinite lower triangular matrices. EXAMPLE First few rows of the triangle are:    1;    3,  1;    4,  0, 1;    7,  3, 0, 1;    6,  0, 0, 0, 1;   12,  4, 3, 0, 0, 1;    8,  0, 0, 0, 0, 0, 1;   15,  7, 0, 3, 0, 0, 0, 1;   13,  0, 4, 0, 0, 0, 0, 0, 1;   18,  6, 0, 0, 3, 0, 0, 0, 0, 1;   12,  0, 0, 0, 0, 0, 0, 0, 0, 0, 1;   28, 12, 7, 4, 0, 3, 0, 0, 0, 0, 0, 1;   14,  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;   24,  8, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 1;   24,  0, 6, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;   31, 15, 0, 7, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 1; ... Extended by Omar E. Pol, Nov 19 2019 CROSSREFS Cf. A000203, A007429, A127093, A125093, A244051, A288417, A327096. Sequence in context: A174382 A123730 A143317 * A076816 A021765 A267187 Adjacent sequences:  A130537 A130538 A130539 * A130541 A130542 A130543 KEYWORD nonn,tabl AUTHOR Gary W. Adamson, Jun 03 2007 EXTENSIONS New name and more terms from Omar E. Pol, Nov 19 2019 STATUS approved

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Last modified May 11 13:41 EDT 2021. Contains 343791 sequences. (Running on oeis4.)