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A065475
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Natural numbers excluding 2.
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6
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1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| From the following 4 disjoint subsets of natural numbers A = {1}, B = {2}, OP = {odd primes}, C = {composites}, 16 sets are derivable: A000027 versus empty set, A002808 vs A008578, A065091 vs A065090, A000040 vs A018252, A006005 vs {{2} with A002808}, {1} vs {A000027 excluding 1}, {2} versus this sequence, {1, 2} versus Union[OP, C].
a(n) is the sum of the obvious divisors of n, which are 1 and n.
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FORMULA
| Partial sums of A097330. G.f. : (1+x-x^2)/(1-x)^2 - Paul Barry (pbarry(AT)wit.ie), Aug 05 2004
a(n) = A000203(n) - A048050(n).
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MAPLE
| restart:printlevel := -1; a := [1]; T := x->LambertW(-x); f := series(((1+T(x)))/(1-T(x)), x, 77); for m from 3 to 77 do a := [op(a), op(2*m, f)] od; print(a); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 28 2009]
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CROSSREFS
| Cf. A000027, A002808, A008578, A065091, A065090, A000040, A018252, A006005, A002808.
Sequence in context: A184985 A114637 A009056 * A062983 A081311 A053233
Adjacent sequences: A065472 A065473 A065474 * A065476 A065477 A065478
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KEYWORD
| nonn,easy
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Nov 16 2001
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EXTENSIONS
| Incorrect formula removed by Charles R Greathouse IV (charles.greathouse(AT)case.edu), Mar 18 2010
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