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A076413
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Number of ways n is expressible as the least common multiple of a nonempty set of positive integers not containing either 1 or n.
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1
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0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 6, 0, 1, 1, 0, 0, 6, 0, 6, 1, 1, 0, 28, 0, 1, 0, 6, 0, 45, 0, 0, 1, 1, 1, 72, 0, 1, 1, 28, 0, 45, 0, 6, 6, 1, 0, 120, 0, 6, 1, 6, 0, 28, 1, 28, 1, 1, 0, 850, 0, 1, 6, 0, 1, 45, 0, 6, 1, 45, 0, 672, 0, 1, 6, 6, 1, 45, 0, 120, 0, 1, 0, 850, 1, 1, 1, 28, 0, 850, 1, 6, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,12
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FORMULA
| a(n) = A076078(n)/2 - 2^(d(n)-2), where d(n)=A000005(n) is the number of divisors of n.
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EXAMPLE
| a(12)=6; the 6 sets are: {3,4}, {4,6}, {2,3,4}, {2,4,6}, {3,4,6}, {2,3,4,6}.
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MATHEMATICA
| a076078[n_] := Module[{d, i}, d=Divisors[n]; Sum[MoebiusMu[n/d[[i]]]*(2^DivisorSigma[0, d[[i]]]-1), {i, 1, Length[d]}]]; a[n_] := a076078[n]/2-2^(DivisorSigma[0, n]-2)
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CROSSREFS
| Cf. A076078.
Sequence in context: A137785 A199568 A134899 * A154305 A158781 A195398
Adjacent sequences: A076410 A076411 A076412 * A076414 A076415 A076416
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KEYWORD
| nonn
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com) and Dean Hickerson (dean.hickerson(AT)yahoo.com), Oct 09 2002
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