A069763 Frobenius number of the numerical semigroup generated by consecutive cubes.

181, 1637, 7811, 26659, 73529, 174761, 372007, 727271, 1328669, 2296909, 3792491, 6023627, 9254881, 13816529, 20114639, 28641871, 39988997, 54857141, 74070739, 98591219, 129531401, 168170617, 215970551, 274591799, 345911149

Offset: 2

Author

Victoria A Sapko (vsapko(AT)canes.gsw.edu), Apr 18 2002

Keywords

• easy
• nonn

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 has the formula ab-a-b.

Examples

			a(2)=181 because 181 is not a nonnegative linear combination of 8 and 27, but all integers greater than 181 are.
		

Links

• R. Fröberg, C. Gottlieb and R. Häggkvist, On numerical semigroups, Semigroup Forum, 35 (1987), 63-83 (for definition of Frobenius number).

Crossrefs

Cf. A000578, A037165, A059769, A069755-A069764.

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]