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A059376
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Jordan function J_3(n).
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25
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1, 7, 26, 56, 124, 182, 342, 448, 702, 868, 1330, 1456, 2196, 2394, 3224, 3584, 4912, 4914, 6858, 6944, 8892, 9310, 12166, 11648, 15500, 15372, 18954, 19152, 24388, 22568, 29790, 28672, 34580, 34384, 42408, 39312, 50652, 48006, 57096
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OFFSET
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1,2
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REFERENCES
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L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 199, #3.
R. Sivaramakrishnan, "The many facets of Euler's totient. II. Generalizations and analogues", Nieuw Arch. Wisk. (4) 8 (1990), no. 2, 169-187.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
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FORMULA
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Multiplicative with a(p^e) = p^(3e)-p^(3e-3). - Vladeta Jovovic, Jul 26 2001
a(n)=sum(d|n, d^3*mu(n/d)) - Benoit Cloitre, Apr 05 2002
Dirichlet generating function: zeta(s-3)/zeta(s). - Franklin T. Adams-Watters, Sep 11 2005
A063453(n) divides a(n). - R. J. Mathar, Mar 30 2011
a(n) = Sum_{k=1..n} GCD(k,n)^3 * Cos(2*Pi*k/n). - Enrique Pérez Herrero, Jan 18 2013
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MAPLE
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J := proc(n, k) local i, p, t1, t2; t1 := n^k; for p from 1 to n do if isprime(p) and n mod p = 0 then t1 := t1*(1-p^(-k)); fi; od; t1; end; # (with k = 3)
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MATHEMATICA
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JordanJ[n_, k_: 1] := DivisorSum[n, #^k*MoebiusMu[n/#] &]; f[n_] := JordanJ[n, 3]; Array[f, 39]
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PROG
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(PARI) for(n=1, 120, print1(sumdiv(n, d, d^3*moebius(n/d)), ", "))
(PARI) { for (n = 1, 1000, write("b059376.txt", n, " ", sumdiv(n, d, d^3*moebius(n/d))); ) } [Harry J. Smith, Jun 26 2009]
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CROSSREFS
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See A059379 and A059380 (triangle of values of J_k(n)), A000010 (J_1), A059376 (J_3), A059377 (J_4), A059378 (J_5).
Sequence in context: A063153 A063578 A063159 * A206481 A049453 A211645
Adjacent sequences: A059373 A059374 A059375 * A059377 A059378 A059379
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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, Jan 28 2001
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STATUS
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approved
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