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A064176
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Infinitary Moebius function of n (A064179) equals 1.
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4
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1, 6, 8, 10, 12, 14, 15, 18, 20, 21, 22, 26, 27, 28, 32, 33, 34, 35, 36, 38, 39, 44, 45, 46, 48, 50, 51, 52, 55, 57, 58, 62, 63, 64, 65, 68, 69, 74, 75, 76, 77, 80, 82, 85, 86, 87, 91, 92, 93, 94, 95, 98, 99, 100, 106, 111, 112, 115, 116, 117, 118, 119, 120, 122, 123, 124
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OFFSET
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1,2
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COMMENTS
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The Moebius inversion formula seems to also hold for iMoebiusMu[].
The sequence contains products of even number of distinct terms of A050376. [From Vladimir Shevelev, May 04 2010]
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REFERENCES
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J. Lambek and L. Moser, On some two way classifications of integers, Canad. Math. Bull. 2 (1959), 85-89.
J. Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 22.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..10000
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EXAMPLE
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mu[45]=0 but iMoebiusMu[45]=1 because 45 = 3^2 * 5^1 and the binary digits of 2 and 1 add up to 2, an even number.
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MATHEMATICA
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iMoebiusMu[ n_ ] := Switch[ MoebiusMu[ n ], 1, 1, -1, -1, 0, If[ OddQ[ Plus@@(DigitCount[ Last[ Transpose[ FactorInteger[ n ] ] ], 2, 1 ]) ], -1, 1 ] ];
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CROSSREFS
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Complement of A064175. Cf. A000028, A000379.
Sequence in context: A089229 A123240 A131181 * A000379 A176525 A065985
Adjacent sequences: A064173 A064174 A064175 * A064177 A064178 A064179
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KEYWORD
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nonn,nice,easy
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AUTHOR
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Wouter Meeussen, Sep 17 2001
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STATUS
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approved
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