A332778 a(1) = 1; a(n) = Sum_{d|n, d < n} phi(n/d) * a(d)^2.

1, 1, 2, 3, 4, 8, 6, 15, 14, 24, 10, 96, 12, 48, 56, 255, 16, 344, 18, 656, 108, 120, 22, 9840, 84, 168, 434, 2448, 28, 4608, 30, 65535, 260, 288, 264, 137376, 36, 360, 360, 432512, 40, 16776, 42, 14720, 7208, 528, 46, 96974880, 258, 9464, 608, 28656, 52, 425864, 600

Offset

1,3

Links

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

Formula

a(1) = 1; a(n) = Sum_{k=1..n-1} a(gcd(n, k))^2.

Mathematica

a[1] = 1; a[n_] := Sum[If[d < n, EulerPhi[n/d] a[d]^2, 0], {d, Divisors[n]}]; Table[a[n], {n, 1, 55}]
a[1] = 1; a[n_] := Sum[a[GCD[n, k]]^2, {k, 1, n - 1}]; Table[a[n], {n, 1, 55}]

Crossrefs

Cf. A000010, A006874, A007018, A023900, A069097, A082588.

Sequence in context: A300868 A349239 A176077 * A263694 A210743 A210750

Adjacent sequences: A332775 A332776 A332777 * A332779 A332780 A332781

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 23 2020

Status

approved