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 A065475 Natural numbers excluding 2. 10
 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; text; internal format)
 OFFSET 1,2 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. The natural numbers excluding 2 are the order numbers of magic squares. Order 2 magic squares do not exist. - William Walkington, Mar 12 2016 The numbers occurring at least twice in Pascal's triangle (A007318, A003016). - Rick L. Shepherd, Jun 05 2016 LINKS Wikipedia, Magic square. Index entries for linear recurrences with constant coefficients, signature (2,-1). FORMULA Partial sums of A097330. G.f.: (1+x-x^2)/(1-x)^2. - Paul Barry, Aug 05 2004 a(n) = A000203(n) - A048050(n). a(n) = n+1 for n>1, a(n) = a(n-1)+1 for n>2. - Wesley Ivan Hurt, Mar 13 2016 E.g.f.: (x + 1)*(exp(x) - 1). - Ilya Gutkovskiy, Jun 05 2016 MAPLE printlevel := -1; a := ; 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); # Zerinvary Lajos, Mar 28 2009 MATHEMATICA Join[{1}, Range[3, 100]] (* Wesley Ivan Hurt, Mar 13 2016 *) PROG (PARI) a(n)=n+(n>1) \\ Charles R Greathouse IV, Sep 01 2015 (PARI) x='x+O('x^99); Vec((1+x-x^2)/(1-x)^2) \\ Altug Alkan, Mar 26 2016 (MAGMA) &cat[, [n : n in [3..100]]]; // Wesley Ivan Hurt, Mar 13 2016 CROSSREFS Cf. A000027, A000040, A000203, A002808, A006005, A008578, A018252, A048050, A065090, A065091, A097330. A003016, A007318. Sequence in context: A184985 A114637 A009056 * A062983 A081311 A053233 Adjacent sequences:  A065472 A065473 A065474 * A065476 A065477 A065478 KEYWORD nonn,easy AUTHOR Labos Elemer, Nov 16 2001 EXTENSIONS Incorrect formula removed by Charles R Greathouse IV, Mar 18 2010 STATUS approved

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Last modified April 20 06:59 EDT 2021. Contains 343125 sequences. (Running on oeis4.)