Search: id:A061391
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%I A061391
%S A061391 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,
%T A061391 22,60,5,125,5,51,25,25,25,144,5,25,25,110,5,125,5,60,60,25,5,175,12,
%U A061391 60,25,60,5,110,25,110,25,25,5,300,5,25,60,70,25,125,5,60,25,125,5,264
%N A061391 t(n,3) = Sum_{d|n} tau(d^3), where tau(n) = number of divisors of n, 
               cf. A000005.
%F A061391 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).
%F A061391 a(n) = sum( d dividing n, tau(nd)) - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Nov 30 2002
%F A061391 Dirichlet g.f.: zeta^6(x)
%F A061391 Also tau_6(n) (see A007426)
%F A061391 Multiplicative with a(p^e) = (e+6 choose e). Mitch Harris (Harris.Mitchell(AT)mgh.harvard.edu) 
               Jun 27, 2005.
%e A061391 For k=2 we get an interesting identity: Sum_{d|n} tau(d^2)=(tau(n))^2, 
               cf. A048691, A035116.
%Y A061391 Cf. t(n, 0) = A000005(n), t(n, 1) = A007425(n), t(n, 2) = A035116(n).
%Y A061391 Sequence in context: A121849 A164930 A098331 this_sequence A123133 A122213 
               A049735
%Y A061391 Adjacent sequences: A061388 A061389 A061390 this_sequence A061392 A061393 
               A061394
%K A061391 nonn,mult
%O A061391 1,2
%A A061391 Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 29 2001

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