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A065960 a(n) = n^4*Product_{distinct primes p dividing n} (1+1/p^4). 5

%I

%S 1,17,82,272,626,1394,2402,4352,6642,10642,14642,22304,28562,40834,

%T 51332,69632,83522,112914,130322,170272,196964,248914,279842,356864,

%U 391250,485554,538002,653344,707282,872644,923522,1114112,1200644

%N a(n) = n^4*Product_{distinct primes p dividing n} (1+1/p^4).

%H E. Pérez Herrero, <a href="/A065960/b065960.txt">Table of n, a(n) for n=1..10000</a>

%H F. A. Lewis and others, <a href="https://www.jstor.org/stable/2303350">Problem 4002</a>, Amer. Math. Monthly, Vol. 49, No. 9, Nov. 1942, pp. 618-619.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Dedekind_psi_function">Dedekind Psi function</a>

%F Multiplicative with a(p^e) = p^(4*e)+p^(4*e-4). - _Vladeta Jovovic_, Dec 09 2001

%F a(n) = n^4*sum(d|n, mu(d)^2/d^4). - _Benoit Cloitre_, Apr 07 2002

%F 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

%F Dirichlet g.f.: zeta(s)*zeta(s-4)/zeta(2*s). - _R. J. Mathar_, Jun 06 2011

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

%p seq(A065960(n),n=1..20) ; # _R. J. Mathar_, Jun 06 2011

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

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

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

%K nonn,mult

%O 1,2

%A _N. J. A. Sloane_, Dec 08 2001

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Last modified August 3 20:08 EDT 2020. Contains 336201 sequences. (Running on oeis4.)