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A065959 a(n) = n^3*Product_{distinct primes p dividing n} (1+1/p^3). 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

E. Pérez Herrero,Table of n, a(n) for n=1..10000

F. A. Lewis and others, Problem 4002, Amer. Math. Monthly, Vol. 49, No. 9, Nov. 1942, pp. 618-619.

Wikipedia, Dedekind psi function

FORMULA

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). [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

MATHEMATICA

JordanTotient[n_, k_:1] := DivisorSum[n, #^k * MoebiusMu[n/#] &]/; (n>0) && IntegerQ[n]; A065959[n_] := JordanTotient[n, 6] / JordanTotient[n, 3]; Array[A065959, 39] (* Enrique Pérez Herrero, Aug 22 2010 *)

PROG

(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

CROSSREFS

Cf. A000010, A001615, A007434, A065958.

Sequence in context: A034677 A009255 A062451 * A226333 A017669 A277065

Adjacent sequences:  A065956 A065957 A065958 * A065960 A065961 A065962

KEYWORD

nonn,mult

AUTHOR

N. J. A. Sloane, Dec 08 2001

STATUS

approved

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Last modified December 5 05:27 EST 2016. Contains 278761 sequences.