A112284 A112283/n.

1, 1, 1, 2, 1, 12, 1, 3, 1, 13, 1, 22, 1, 12, 14, 19, 1, 9, 1, 27, 18, 31, 1, 19, 1, 49, 1, 12, 1, 59, 1, 17, 61, 27, 15, 14, 1, 98, 6, 7, 1, 12, 1, 95, 45, 9, 1, 17, 1, 26, 73, 23, 1, 18, 10, 35, 69, 17, 1, 108, 1, 29, 65, 28, 47

Offset: 1

Author

Paul D. Hanna and Robert G. Wilson v, Aug 20 2005

Keywords

• hard
• nonn

Crossrefs

Cf. A109626, A112283.

Programs

Mathematica

f[n_] := Module[{j = 1, a}, a[0] = 1; a[l_] := a[l] = Block[{k = 1, s = Sum[ a[i]*x^i, {i, 0, l - 1}]}, While[ IntegerQ[ Last[ CoefficientList[ Series[(s + k*x^l)^(1/n), {x, 0, l}], x]]] != True, k++ ]; k]; While[a[j] != 1, j++ ]; j]; Table[ f[n]/n, {n, 10}]

Formula

Conjecture: a(n)=1 iff n is 1, a prime or the square of an odd prime.

Extensions

a(30)-a(50) from Robert G. Wilson v, Oct 29 2007

a(51)-a(65) from Robert G. Wilson v, Jul 25 2008