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

2,1

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

Table of n, a(n) for n=2..26.

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

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

Sequence in context: A268520 A235975 A137530 * A264289 A200953 A264337

Adjacent sequences: A069760 A069761 A069762 * A069764 A069765 A069766

Keyword

easy,nonn

Author

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

Status

approved