A111614 First upper diagonal of array in A109626.

1, 1, 1, 3, 1, 6, 1, 7, 1, 3, 1, 6, 1, 3, 12, 3, 1, 6, 1, 11, 18, 3, 1, 24, 1, 3, 1, 8, 1, 21, 1, 11, 20, 20, 23, 16, 1, 22, 34, 21, 1, 14, 1, 22, 24, 26, 1, 2, 1, 43, 6, 26, 1, 33, 17, 46, 43, 32, 1, 25, 1, 34, 47, 35, 63, 25, 1, 8, 49, 31, 1, 48, 1, 40, 32, 73, 21, 58, 1, 80, 28, 44, 1, 29

Offset: 1

Author

Paul D. Hanna and Robert G. Wilson v, Jul 30 2005

Keywords

• nonn

Comments

a(1) = a(2) = 1 and a(p^e) = 1 for odd primes p and noncomposite exponents e.

a(81) = 28 and not 1 because 9^2 = 81.

Crossrefs

Cf. A109626.

Programs

Mathematica

f[n_] := f[n] = Block[{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]; Table[a[j], {j, 0, 128}]]; g[n_, m_] := f[n][[m]]; Table[ g[n, n + 1], {n, 84}]