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A061391
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t(n,3) = Sum_{d|n} tau(d^3), where tau(n) = number of divisors of n, cf. A000005.
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3
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1, 5, 5, 12, 5, 25, 5, 22, 12, 25, 5, 60, 5, 25, 25, 35, 5, 60, 5, 60, 25, 25, 5, 110, 12, 25, 22, 60, 5, 125, 5, 51, 25, 25, 25, 144, 5, 25, 25, 110, 5, 125, 5, 60, 60, 25, 5, 175, 12, 60, 25, 60, 5, 110, 25, 110, 25, 25, 5, 300, 5, 25, 60, 70, 25, 125, 5, 60, 25, 125, 5, 264
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Inverse Mobius transform of A048785. - R. J. Mathar, Feb 09 2011
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FORMULA
| t(n, k) = Sum_{d|n} tau(d^k) is multiplicative: if the canonical factorization of n = Product p^e(p) over primes then t(n, k) = Product t(p^e(p), k), t(p^e(p), k) = (1/2) *(k*e(p)+2)*(e(p)+1).
a(n) = sum( d dividing n, tau(nd)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 30 2002
Multiplicative with a(p^e) = (e+6 choose e). Mitch Harris (Harris.Mitchell(AT)mgh.harvard.edu) Jun 27, 2005.
sum(n=1,infinity,tau(n^3)*x^n/(1-x^n)).
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EXAMPLE
| For k=2 we get an interesting identity: Sum_{d|n} tau(d^2)=(tau(n))^2, cf. A048691, A035116.
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CROSSREFS
| Cf. t(n, 0) = A000005(n), t(n, 1) = A007425(n), t(n, 2) = A035116(n).
Sequence in context: A164930 A173316 A098331 * A168336 A123133 A206553
Adjacent sequences: A061388 A061389 A061390 * A061392 A061393 A061394
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KEYWORD
| nonn,mult
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 29 2001
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