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 A084067 Integer coefficients of A(x), where 1<=a(n)<=12, such that A(x)^(1/12) consists entirely of integer coefficients. 12
 1, 12, 6, 4, 9, 12, 4, 12, 12, 8, 6, 12, 6, 12, 12, 12, 12, 12, 8, 12, 9, 12, 12, 12, 12, 12, 6, 12, 6, 12, 10, 12, 6, 12, 12, 12, 2, 12, 6, 8, 6, 12, 12, 12, 12, 4, 12, 12, 8, 12, 12, 8, 3, 12, 4, 12, 12, 4, 12, 12, 9, 12, 6, 4, 6, 12, 4, 12, 12, 12, 12, 12, 2, 12, 6, 12, 3, 12, 6, 12, 3, 8 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS More generally, the sequence: "integer coefficients of A(x), where 1<=a(n)<=m, such that A(x)^(1/m) consists entirely of integer coefficients", appears to have a unique solution for all m>0. Are these sequences ever periodic? LINKS Robert G. Wilson v, Table of n, a(n) for n = 0..3000. MATHEMATICA a[0] = 1; a[n_] := a[n] = Block[{k = 1, s = Sum[a[i]*x^i, {i, 0, n-1}]}, While[ Union[ IntegerQ /@ CoefficientList[ Series[(s+k*x^n)^(1/12), {x, 0, n}], x]] != {True}, k++ ]; k]; Table[ a[n], {n, 0, 81}] (* Robert G. Wilson v *) CROSSREFS Cf. A083952, A083953, A083954, A083955, A083956, A083947 A083948, A083949, A083950, A084066. Sequence in context: A051725 A070292 A283880 * A240537 A227354 A328043 Adjacent sequences: A084064 A084065 A084066 * A084068 A084069 A084070 KEYWORD nonn AUTHOR Paul D. Hanna, May 10 2003 EXTENSIONS More terms from Robert G. Wilson v, Jul 26 2005 STATUS approved

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Last modified June 18 11:09 EDT 2024. Contains 373481 sequences. (Running on oeis4.)