A338750 a(n) = 1 + Sum_{k=1..n-1} a(gcd(n,k)).

1, 2, 3, 5, 5, 10, 7, 14, 13, 18, 11, 35, 13, 26, 31, 41, 17, 58, 19, 65, 45, 42, 23, 122, 41, 50, 63, 95, 29, 154, 31, 122, 73, 66, 83, 241, 37, 74, 87, 230, 41, 226, 43, 155, 193, 90, 47, 419, 85, 194, 115, 185, 53, 338, 135, 338, 129, 114, 59, 679, 61, 122, 283

Offset

1,2

Comments

Inverse Moebius transform of A006874.

Links

Table of n, a(n) for n=1..63.

Formula

G.f. A(x) satisfies: A(x) = x / (1 - x) + Sum_{k>=2} phi(k) * A(x^k).

a(n) = 1 + Sum_{d|n, d < n} phi(n/d) * a(d).

a(n) = Sum_{d|n} A006874(d).

Mathematica

a[n_] := a[n] = 1 + Sum[a[GCD[n, k]], {k, 1, n - 1}]; Table[a[n], {n, 1, 63}]
a[n_] := a[n] = 1 + DivisorSum[n, EulerPhi[n/#] a[#] &, # < n &]; Table[a[n], {n, 1, 63}]

Crossrefs

Cf. A000010, A006874, A038045, A130054.

Sequence in context: A237365 A322770 A257008 * A265822 A257012 A325412

Adjacent sequences: A338747 A338748 A338749 * A338751 A338752 A338753

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 06 2020

Status

approved