OFFSET
2,1
COMMENTS
The Frobenius number of a numerical semigroup generated by relatively prime integers a_1,...,a_n is the largest positive integer that is not a nonnegative linear combination of a_1,...,a_n. Since consecutive cubes are relatively prime, they generate a numerical semigroup with a Frobenius number. The Frobenius number of a 2-generated semigroup <a,b> has the formula ab-a-b.
LINKS
R. Fröberg, C. Gottlieb and R. Häggkvist, On numerical semigroups, Semigroup Forum, 35 (1987), 63-83 (for definition of Frobenius number).
FORMULA
a(n) = n^3*(n+1)^3-n^3-(n+1)^3 = n^6+3*n^5+3*n^4-n^3-3*n^2-3*n-1.
G.f.: x^2*(181+370*x+153*x^2+24*x^3-13*x^4+6*x^5-x^6)/(1-x)^7. [Colin Barker, Feb 14 2012]
EXAMPLE
a(2)=181 because 181 is not a nonnegative linear combination of 8 and 27, but all integers greater than 181 are.
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Victoria A Sapko (vsapko(AT)canes.gsw.edu), Apr 18 2002
STATUS
approved