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A034695
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Dirichlet convolution of number-of-divisors function (A000005) with A007426.
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13
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1, 6, 6, 21, 6, 36, 6, 56, 21, 36, 6, 126, 6, 36, 36, 126, 6, 126, 6, 126, 36, 36, 6, 336, 21, 36, 56, 126, 6, 216, 6, 252, 36, 36, 36, 441, 6, 36, 36, 336, 6, 216, 6, 126, 126, 36, 6, 756, 21, 126, 36, 126, 6, 336, 36, 336, 36, 36, 6, 756, 6, 36, 126, 462, 36, 216, 6, 126
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n) is also tau_6 (the 6th Piltz divisor function), where tau_5 is A061200, and A000005 is tau_2
a(n) is the number of ordered 6-factorizations of n.
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REFERENCES
| T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, pages 29 and 38
Leveque, William J., Fundamentals of Number Theory. New York:Dover Publications, 1996, ISBN 9780486689067, p .167-Exercise 5.b.
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LINKS
| E. Pérez Herrero, Piltz Divisor functions (1), Psychedelic Geometry Blogspot, Dec 21 2009
E. Pérez Herrero, Piltz Divisor functions (2), Psychedelic Geometry Blogspot, Dec 24 2009
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FORMULA
| Dirichlet g.f.: zeta^6(x)
Multiplicative with a(p^e) = (e+5 choose e). Mitch Harris (Harris.Mitchell(AT)mgh.harvard.edu) Jun 27, 2005.
The Piltz divisor functions hold for tau_j(*)tau_k = tau_{j+k}, where (*) means Dirichlet´s functional convolution.
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MATHEMATICA
| tau[n_, 1] = 1; tau[n_, k_] := tau[n, k] = Plus @@ (tau[ #, k - 1] & /@ Divisors[n]); Table[ tau[n, 6], {n, 68}] (* Robert G. Wilson v *)
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CROSSREFS
| Sequence in context: A045896 A115046 A004983 * A198340 A189980 A188273
Adjacent sequences: A034692 A034693 A034694 * A034696 A034697 A034698
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KEYWORD
| nonn,mult
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(at)rgwv.com), Nov 02 2005
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