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A053864
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A second order generalization of the Mobius function of n.
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3
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1, 1, 1, -1, 1, 1, 1, 0, -1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, -1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, -1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Contribution R. J. Mathar, Apr 15 2011 (Start):
K-th order generalizations of the Mobius function are defined here (k=2), in A053865 (k=3) and A053981 (k=4) as follows:
The arithmetic function is 0 if the canonical prime power factorization of n contains an exponent >k. Otherwise, the function is 1 if any exponent is < k. In the remaining cases the function is (-1)^omega(n), where omega = A001221 counts the number of distinct primes dividing n.
The function is not multiplicative (example: a(3)= +1, a(4)= -1 and a(12)= +1). (End)
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MAPLE
| with(numtheory); k := 2; A053864 := proc(n, k) local t1, t2, i; t1 := 1; if n=1 then RETURN(t1); fi; t2 := factorset(n); for i in t2 do if n mod i^(k+1) = 0 then RETURN(0); fi; od; for i in t2 do if n mod i^k <> 0 then RETURN(1); else t1 := -t1; fi; od; t1; end;
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CROSSREFS
| Cf. A008683, A053865, A053981.
Sequence in context: A118111 A119981 A115789 * A129667 A071374 A071025
Adjacent sequences: A053861 A053862 A053863 * A053865 A053866 A053867
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KEYWORD
| sign
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Apr 08 2000
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