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A065959
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n^3*Product_{distinct primes p dividing n} (1+1/p^3).
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11
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1, 9, 28, 72, 126, 252, 344, 576, 756, 1134, 1332, 2016, 2198, 3096, 3528, 4608, 4914, 6804, 6860, 9072, 9632, 11988, 12168, 16128, 15750, 19782, 20412, 24768, 24390, 31752, 29792, 36864, 37296, 44226, 43344, 54432, 50654, 61740, 61544
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OFFSET
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1,2
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REFERENCES
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F. A. Lewis and others, Problem 4002, Amer. Math. Monthly, Vol. 49, No. 9, Nov. 1942, pp. 618-619.
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LINKS
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E. Pérez Herrero,Table of n, a(n) for n=1..10000
Wikipedia, Dedekind psi function
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FORMULA
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Multiplicative with a(p^e) = p^(3*e)+p^(3*e-3). - Vladeta Jovovic, Dec 09 2001
a(n) = n^3*sum(d|n, mu(d)^2/d^3) - Benoit Cloitre, Apr 07 2002
a(n) = sum(d|n, mu(n/d)^2*d^3). [Joerg Arndt, Jul 06 2011]
a(n)=J_6(n)/J_3(n)=A069091(n)/A059376(n) [From Enrique Pérez Herrero, Aug 22 2010]
Dirichlet g.f. zeta(s)*zeta(s-3)/zeta(2*s). Dirichlet convolution of A008966 and A000578. - R. J. Mathar, Apr 10 2011
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MATHEMATICA
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Contribution from Enrique Pérez Herrero, Aug 22 2010: (Start)
JordanTotient[n_, k_:1]:=DivisorSum[n, #^k*MoebiusMu[n/# ]&]/; (n>0)&&IntegerQ[n];
A065959[n_]:=JordanTotient[n, 6]/JordanTotient[n, 3]; (End)
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PROG
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(PARI) for(n=1, 100, print1(n^3*sumdiv(n, d, moebius(d)^2/d^3), ", "))
(PARI) a(n)=sumdiv(n, d, moebius(n/d)^2*d^3); [Joerg Arndt, Jul 06 2011]
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CROSSREFS
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Cf. A000010, A001615, A007434, A065958.
Sequence in context: A034677 A009255 A062451 * A017669 A001158 A171215
Adjacent sequences: A065956 A065957 A065958 * A065960 A065961 A065962
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KEYWORD
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nonn,mult,changed
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AUTHOR
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N. J. A. Sloane, Dec 08 2001
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STATUS
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approved
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