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Search: id:A060184
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| A060184 |
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Triangle of generalized sum of divisors function, read by rows. |
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+0
5
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| 1, 0, 1, 2, 0, -1, 1, 2, 1, 2, 0, 0, 1, 2, 1, 1, -2, 0, 1, 3, 1, 5, 6, 0, 0, -1, -1, 2, 1, 5, 5, -2, 0, -2, -3, 2, 2, 9, 10, 0, 1, 4, 3, 0, 4, 0, 2, 9, 9, -3, 1, 3, -2, -7, 2, 0, 3, 14, 16, 0, 2, 6, -1, -9, 2, 0, 3, 15, 17, -2, 1, 8, 19, 10, -6, 4, 0, -1, 0, 15, 22, 0, 1, 9, 21, 7, -13, 2, 0, -2, -4, 11, 20, -4, 2, 15, 33, 14, -15, 3, 0, -4, -10, 10, 28, 0, 3
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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Lengths of rows are 1 1 2 2 2 3 3 3 3 4 4 4 4 4 ... (A003056).
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REFERENCES
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P. A. MacMahon, Divisors of numbers and their continuations in the theory of partitions, Proc. London Math. Soc., (2) 19 (1919), 75-113; Coll. Papers II, pp. 303-341.
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FORMULA
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G.f. for k-th diagonal (the k-th row of the sideways triangle shown in the example): Sum_{ m_1 < m_2 < ... < m_k} q^(m_1+m_2+...+m_k)/((1+q^m_1)*(1+q^m_2)*...*(1+q^m_k)) = Sum_n T(n, k)*q^n.
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EXAMPLE
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Triangle turned on its side begins:
.1 0 2 -1 2 0 2 -2 3 .0 .2 etc
.... 1 .0 1 2 1 .1 1 .6 -1 etc
......... 1 0 1 .0 5 -1 .5 etc
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CROSSREFS
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Diagonals give A048272, A060185, A060186. Cf. A060043, A060044, A060047, A060177.
Sequence in context: A117468 A116374 A025911 this_sequence A055639 A156542 A066360
Adjacent sequences: A060181 A060182 A060183 this_sequence A060185 A060186 A060187
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KEYWORD
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sign,tabf,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Mar 20 2001
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EXTENSIONS
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More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 20 2007
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