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A069091
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Jordan function J_6(n).
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10
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1, 63, 728, 4032, 15624, 45864, 117648, 258048, 530712, 984312, 1771560, 2935296, 4826808, 7411824, 11374272, 16515072, 24137568, 33434856, 47045880, 62995968, 85647744, 111608280, 148035888, 187858944, 244125000, 304088904, 386889048
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listen;
history;
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OFFSET
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1,2
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COMMENTS
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Contribution from Enrique Pérez Herrero, Sep 14 2010: (Start)
a(n) is the Moebius transform of n^6
Note that J_2(n), J_3(n), eulerphi(n) and psi(n) divides a(n), this sequences
are: A007434(n), A059376(n), A000010(n) and A001615(n) respectively. (End)
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REFERENCES
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L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 199, #3.
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LINKS
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E. Pérez Herrero,Table of n, a(n) for n=1..2000
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FORMULA
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a(n)=sum(d|n, d^6*mu(n/d))
Multiplicative with a(p^e) = p^(6e)-p^(6(e-1)).
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MATHEMATICA
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Contribution from Enrique Pérez Herrero, Sep 14 2010: (Start)
JordanTotient[n_, k_:1]:=DivisorSum[n, #^k*MoebiusMu[n/# ]&]/; (n>0)&&IntegerQ[n]
A069091[n_IntegerQ]:=JordanTotient[n, 6]; (End)
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PROG
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(PARI) for(n=1, 100, print1(sumdiv(n, d, d^6*moebius(n/d)), ", "))
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CROSSREFS
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Cf. A059379 and A059380 (triangle of values of J_k(n)), A000010 (J_1), A059376 (J_3), A059377 (J_4), A059378 (J_5).
Cf. A065959 [From Enrique Pérez Herrero, Sep 14 2010]
Sequence in context: A198399 A221968 A115152 * A123866 A024004 A201886
Adjacent sequences: A069088 A069089 A069090 * A069092 A069093 A069094
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KEYWORD
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easy,nonn,mult
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AUTHOR
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Benoit Cloitre, Apr 05 2002
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STATUS
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approved
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