A110879 Let a_0 = 1 and for n > 0, let a_n be the smallest positive integer not already in the sequence such that (a_0 + a_1 x + a-2x^2 + ....)^(1/3) has integer coefficients. (Hanna's A083349). Let f(n) = n th term in the present sequence. Then a_0 + a_1 x + a_2 x^2 + ... = (1-x)^f(1) (1-x^2)^f(2) (1-x^3)^f(3) ....

-1, -2, -3, 5, 1, -3, -3, 7, 6, -7, -23, 15, 12, 28, -48, -25, -10, 165, 4, -274, -408, 927, 932, -1179, -3745, 2906, 7620, -1471, -21283, 1593, 40509, 18877, -93870, -53839, 153551, 204285, -293171, -462306, 307359, 1227141, -282147, -2368041, -1025023, 5041701, 4100247, -7457707, -15096708

Offset: 1

Author

Barry Brent (barrybrent(AT)member.ams.org), Sep 19 2005

Keywords

• sign

Comments

The preprint reference asks for a generating function for Hanna's sequence. Terms of present sequence are the exponents in an infinite product for Hanna's sequence. They were obtained from terms of Hanna's sequence with the cited theorem in Apostol and Mobius inversion.

References

• Apostol, T., Introduction to Analytic Number Theory, Springer-Verlag 1976, Theorem 14.8, p. 323.

Links

• N. Heninger, E. M. Rains and N. J. A. Sloane, On the Integrality of n-th Roots of Generating Functions, J. Combinatorial Theory, Series A, 113 (2006), 1732-1745.

Crossrefs

Cf. A083349.