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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) ....
0
-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
1,2
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.
Sequence in context: A256888 A010585 A295302 * A016587 A123217 A039704
KEYWORD
sign
AUTHOR
Barry Brent (barrybrent(AT)member.ams.org), Sep 19 2005
STATUS
approved