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A166698
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Totally multiplicative sequence with a(p) = a(p-1) - 1 for prime p.
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0
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1, 0, -1, 0, -1, 0, -1, 0, 1, 0, -1, 0, -1, 0, 1, 0, -1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, -1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, -1, 0, -1, 0, -1, 0, -1, 0, 1, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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FORMULA
| Multiplicative with a(p^e) = (a(p-1)-1)^e. If n = Product p(k)^e(k) then a(n) = Product (a(p(k)-1)-1)^e(k). Multiplicative with a(p^e) = 0 if p = 2, with a(p^e) = 1 if p > 2 and e is even, with a(p^e) = -1 if p > 2 and e is odd. a(p) = -1 for prime p > 2. a(1) = 1, for k >= 1: a(2k) = 0, a(2k - 1) = 1 if A001222(2k - 1) is even, a(2k - 1) = -1 if A001222(2k - 1) is odd. A001222(n) = bigomega (n). Abs (a(n)) = A000035(n) for n >= 1, i.e. simple periodic sequence. Sum_{d|n} a(d) * A000012(d) = Sum_{d|n} a(d) * A000012(d/n) = A053866(n) = A093709(n) for n>= 1.
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CROSSREFS
| Sequence in context: A015301 A016213 A015757 * A059841 A056594 A101455
Adjacent sequences: A166695 A166696 A166697 * A166699 A166700 A166701
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KEYWORD
| sign,mult
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AUTHOR
| Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Oct 18 2009
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