

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
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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

Table of n, a(n) for n=1..76.
Wikipedia, Magic square.
Index entries for linear recurrences with constant coefficients, signature (2,1).


FORMULA

Partial sums of A097330. G.f.: (1+xx^2)/(1x)^2.  Paul Barry, Aug 05 2004
a(n) = A000203(n)  A048050(n).
a(n) = n+1 for n>1, a(n) = a(n1)+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 := [1]; T := x>LambertW(x); f := series(((1+T(x)))/(1T(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+xx^2)/(1x)^2) \\ Altug Alkan, Mar 26 2016
(MAGMA) &cat[[1], [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



