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A130130
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a(0)=0, a(1)=1, a(n)=2 for n >= 2.
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14
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0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| a(n) is also total number of positive integers below 10^(n+1) requiring 9 positive cubes in their representation as sum of cubes (cf. Dickson, 1939).
A061439(n) + A181375(n) + A181377(n) + A181379(n) + A181381(n) + A181400(n) + A181402(n) + A181404(n) + a(n) = A002283(n)
a(n) = number of obvious divisors of n. The obvious divisors of n are the numbers 1 and n. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Mar 02 2009]
Number of colors needed to paint n adjacent segments on a line. [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Mar 20 2009]
a(n) = ceiling(n-th nonprimes/n) = ceiling(A018252(n)/A000027(n)) for n >= 1. Numerators of (A018252(n)/A000027(n)) in A171529(n), denominators of (A018252(n)/A000027(n)) in A171530(n). a(n) = A171624(n) + 1 for n >= 5. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Dec 13 2009]
a(n) is also the continued fraction for sqrt(1/2) [From Enrique Perez Herrero (psychgeometry(AT)gmail.com), Jul 12 2010]
Conjecture: for n >= 1, a(n) = minimal number of divisors of any n-digit number. See A066150 - maximal number of divisors of any n-digit number. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Jul 18 2010]
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REFERENCES
| Dickson, Leonard Eugene: All integers except 23 and 239 are sums of eight cubes. In: Bulletin of the American Mathematical Society 45 (1939), p. 588-591.
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LINKS
| Weisstein, Eric W.: MathWorld -- Waring's Problem.
Index to sequences with linear recurrences with constant coefficients, signature (1).
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FORMULA
| a(n)=2*[(n+2) mod (n+1)]-[n!^2 mod (n+1)]*[(n+1)!^2 mod (n+2)], with n>=0. - Paolo P. Lava (paoloplava(AT)gmail.com), Aug 28 2007
G.f.: x*(1+x)/(1-x)=x*(1-x^2)/(1-x)^2 [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Mar 20 2009]
a(n) = A000005(n) - A070824(n) for n >= 1.
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MATHEMATICA
| Contribution from Enrique Perez Herrero (psychgeometry(AT)gmail.com), Jul 12 2010: (Start)
A130130[0]:=0;
A130130[1]:=1;
A130130[n_]:=2;
(*Other method*)
A130130[n_]:=ContinuedFraction[Sqrt[1/2], n+1][[n+1]] (End)
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PROG
| (PARI) a(n)=min(n, 2) \\ Charles R Greathouse IV, Jun 01 2011
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CROSSREFS
| Cf. A158411. [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Mar 20 2009]
Sequence in context: A077433 A065685 A084100 * A046698 A007395 A036453
Adjacent sequences: A130127 A130128 A130129 * A130131 A130132 A130133
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KEYWORD
| nonn,easy
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AUTHOR
| Paul Curtz (bpcrtz(AT)free.fr), Aug 01 2007
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