login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A069763 Frobenius number of the numerical semigroup generated by consecutive cubes. 1
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 (list; graph; refs; listen; history; text; internal format)
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.

REFERENCES

R. Froberg, C. Gottlieb and R. Haggkvist, "On numerical semigroups", Semigroup Forum, 35 (1987), 63-83 (for definition of Frobenius number).

LINKS

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

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 10 01:45 EDT 2020. Contains 336363 sequences. (Running on oeis4.)