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 A034695 Tau_6 (the 6th Piltz divisor function), the number of ordered 6-factorizations of n; Dirichlet convolution of number-of-divisors function (A000005) with A007426. 13
 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; text; internal format)
 OFFSET 1,2 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. LINKS Seiichi Manyama, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Enrique Pérez Herrero) 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 FORMULA Dirichlet g.f.: zeta^6(s). Multiplicative with a(p^e) = (e+5 choose e). - Mitch Harris, Jun 27 2005 The Piltz divisor functions hold for tau_j(*)tau_k = tau_{j+k}, where (*) means Dirichlet convolution. G.f.: Sum_{k>=1} tau_5(k)*x^k/(1 - x^k). - Ilya Gutkovskiy, Oct 30 2018 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, Nov 02 2005 *) PROG (PARI) a(n) = my(f=factor(n)); for (i=1, #f~, f[i, 1] = binomial(f[i, 2] + 5, f[i, 2]); f[i, 2]=1); factorback(f); \\ Michel Marcus, Jun 09 2014 CROSSREFS Cf. A000005 (tau_2), A007425 (tau_3), A007426 (tau_4), A061200 (tau_5). Cf. A061204. Column k=6 of A077592. Sequence in context: A115046 A004983 A298936 * A198340 A189980 A188273 Adjacent sequences:  A034692 A034693 A034694 * A034696 A034697 A034698 KEYWORD nonn,mult AUTHOR EXTENSIONS More terms from Robert G. Wilson v, Nov 02 2005 STATUS approved

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Last modified March 24 19:42 EDT 2019. Contains 321448 sequences. (Running on oeis4.)