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Search: id:A059377
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| A059377 |
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Jordan function J_4(n). |
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+0
13
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| 1, 15, 80, 240, 624, 1200, 2400, 3840, 6480, 9360, 14640, 19200, 28560, 36000, 49920, 61440, 83520, 97200, 130320, 149760, 192000, 219600, 279840, 307200, 390000, 428400, 524880, 576000, 707280, 748800, 923520, 983040, 1171200
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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This sequence is multiplicative. - Mitch Harris, Apr 19 2005
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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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a(n)=sum(d|n, d^4*mu(n/d)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 05 2002
Multiplicative with a(p^e) = p^(4e)-p^(4(e-1)).
Dirichlet generating function: zeta(s-4)/zeta(s). - Franklin T. Adams-Watters, Sep 11 2005.
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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 = 4)
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PROGRAM
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(PARI) for(n=1, 100, print1(sumdiv(n, d, d^4*moebius(n/d)), ", "))
(PARI) a(n)=if(n<1, 0, sumdiv(n, d, d^4*moebius(n/d)))
(PARI) a(n)=if(n<1, 0, dirdiv(vector(n, k, k^4), vector(n, k, 1))[n])
(PARI) { for (n = 1, 1000, write("b059377.txt", n, " ", sumdiv(n, d, d^4*moebius(n/d))); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), 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).
See A059379 and A059380 (triangle of values of J_k(n)), A000010 (J_1), A007434 (J_2), A059376 (J_3), A059378 (J_5).
Adjacent sequences: A059374 A059375 A059376 this_sequence A059378 A059379 A059380
Sequence in context: A082540 A085808 A033594 this_sequence A123865 A024002 A050149
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KEYWORD
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nonn,mult
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Jan 28 2001
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