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A114592
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sum{n>=1} a(n)/n^s = product{k>=2} (1 -1/k^s).
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1
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1, -1, -1, -1, -1, 0, -1, 0, -1, 0, -1, 1, -1, 0, 0, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| For n >= 2, sum{k|n} (A001055(n/k)) *a(k) = 0. A114591(n) = sum{k|n} a(k).
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FORMULA
| a(1) = 1; for n>= 2, a(n) = sum, over ways to factor n into any number of distinct integers >= 2, of (-1)^(number of integers in a factorization). (See example.)
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EXAMPLE
| 24 can be factored into distinct integers (each >= 2) as 24; as 4*6, 3*8 and 2*12; and as 2*3*4..
So a(24) = (-1)^1 + 3*(-1)^2 + (-1)^3 = 1, where the 1 exponent is due to the 1 factor of the 24 = 24 factorization and the 2 exponent is due to the 3 cases of 2 factors each of the 24 = 4*6 = 3*8 = 2*12 factorizations and the 3 exponent is due to the 24 = 2*3*4 factorization.
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CROSSREFS
| Cf. A001055, A114591.
Sequence in context: A071034 A089497 A089496 * A140653 A071036 A118110
Adjacent sequences: A114589 A114590 A114591 * A114593 A114594 A114595
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KEYWORD
| more,sign
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AUTHOR
| Leroy Quet, Dec 11 2005
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