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A065960 n^4*Product_{distinct primes p dividing n} (1+1/p^4). 3
1, 17, 82, 272, 626, 1394, 2402, 4352, 6642, 10642, 14642, 22304, 28562, 40834, 51332, 69632, 83522, 112914, 130322, 170272, 196964, 248914, 279842, 356864, 391250, 485554, 538002, 653344, 707282, 872644, 923522, 1114112, 1200644 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

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

LINKS

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

Wikipedia, Dedekind Psi function

FORMULA

Multiplicative with a(p^e) = p^(4*e)+p^(4*e-4). - Vladeta Jovovic, Dec 09 2001

a(n) = n^4*sum(d|n, mu(d)^2/d^4). - Benoit Cloitre, Apr 07 2002

a(n)=J_8(n)/J_4(n)=A069093(n)/A059377(n), where J_k is the k-th Jordan Totient Function. - Enrique Pérez Herrero, Aug 29 2010

Dirichlet g.f. zeta(s)*zeta(s-4)/zeta(2*s). - R. J. Mathar, Jun 06 2011

MAPLE

A065960 := proc(n) n^4*mul(1+1/p^4, p=numtheory[factorset](n)) ; end proc:

seq(A065960(n), n=1..20) ; # R. J. Mathar, Jun 06 2011

MATHEMATICA

a[n_] := n^4*DivisorSum[n, MoebiusMu[#]^2/#^4&]; Array[a, 40] (* Jean-François Alcover, Dec 01 2015 *)

PROG

(PARI) for(n=1, 100, print1(n^4*sumdiv(n, d, moebius(d)^2/d^4), ", "))

CROSSREFS

Cf. A000010, A001615, A007434, A065959, A065958.

Sequence in context: A184982 A088687 A034678 * A017671 A001159 A053820

Adjacent sequences:  A065957 A065958 A065959 * A065961 A065962 A065963

KEYWORD

nonn,mult

AUTHOR

N. J. A. Sloane, Dec 08 2001

STATUS

approved

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Last modified December 10 00:24 EST 2016. Contains 278993 sequences.