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A092342
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a(n) = sigma_3(3n+1).
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4
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1, 73, 344, 1134, 2198, 4681, 6860, 11988, 15751, 25112, 29792, 44226, 50654, 73710, 79508, 109512, 117993, 160454, 167832, 219510, 226982, 299593, 300764, 390096, 389018, 500780, 493040, 620298, 619164, 779220, 756112, 934416, 912674, 1149823, 1092728
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| Expansion of q^(-1/3) * c(q) * (c(q)^3 + b(q)^3 / 3) in powers of q where b(), c() are cubic AGM functions. - Michael Somos Aug 22 2007
If b(3*n) = 0, b(3*n+1) = a(n), b(3*n+2) = A092343(n), then b(n) is multiplicative with b(3^e) = 0^e, b(p^e) = (p^(3*e+3) - 1) / (p^3 - 1) otherwise. - Michael Somos Aug 22 2007
a(n) = A000731(n) + 81*A033690(n-1). - Michael Somos Aug 22 2007
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EXAMPLE
| q + 73*q^4 + 344*q^7 + 1134*q^10 + 2198*q^13 + 4681*q^16 + ...
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PROG
| (PARI) {a(n) = if(n<0, 0, sigma(3*n+1, 3))} /* Michael Somos Aug 22 2007 */
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CROSSREFS
| Trisection of A001158. Cf. A045823, A091986, A092341, A092343.
Sequence in context: A005108 A142810 A142279 * A170916 A200908 A142229
Adjacent sequences: A092339 A092340 A092341 * A092343 A092344 A092345
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Mar 20 2004
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