This site is supported by donations to The OEIS Foundation.

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.