A372618 a(1) = a(2) = 1; a(n+2) = Sum_{k=1..n} a(gcd(n,k)).

1, 1, 1, 2, 3, 5, 7, 10, 13, 18, 21, 29, 31, 46, 43, 65, 61, 91, 77, 128, 95, 172, 127, 213, 149, 292, 181, 347, 231, 437, 259, 562, 289, 679, 361, 772, 431, 991, 467, 1104, 565, 1352, 605, 1613, 647, 1877, 835, 2048, 881, 2529, 965, 2802, 1135, 3216, 1187

Offset

1,4

Links

Table of n, a(n) for n=1..55.

Formula

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

a(1) = a(2) = 1; a(n+2) = Sum_{d|n} phi(n/d) * a(d).

Mathematica

a[1] = a[2] = 1; a[n_] := a[n] = Sum[a[GCD[n - 2, k]], {k, 1, n - 2}]; Table[a[n], {n, 1, 55}]
nmax = 55; A[_] = 0; Do[A[x_] = x + x^2 (1 + Sum[EulerPhi[k] A[x^k], {k, 1, nmax}]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] // Rest

Crossrefs

Cf. A000010, A006874, A038045.

Sequence in context: A177332 A318155 A282569 * A213213 A319470 A115001

Adjacent sequences: A372615 A372616 A372617 * A372619 A372620 A372621

Keyword

nonn

Author

Ilya Gutkovskiy, May 07 2024

Status

approved