A038045 Shifts left under transform T where Ta is phi DCONV a.

1, 1, 2, 4, 7, 11, 17, 23, 33, 43, 58, 68, 97, 109, 138, 168, 211, 227, 298, 316, 401, 459, 537, 559, 723, 771, 892, 988, 1173, 1201, 1507, 1537, 1791, 1947, 2190, 2324, 2825, 2861, 3195, 3437, 3999, 4039, 4794, 4836, 5481, 5971, 6552, 6598, 7775

Offset: 1

Author

Christian G. Bower

Keywords

• nonn
• eigen

Comments

Eigensequence of triangle A054523; i.e., multiplication by A054523 shifts the sequence to (1, 2, 4, ...). - Gary W. Adamson, Apr 26 2009

Crossrefs

Cf. A000010, A054523.

Programs

Mathematica

a[1] = 1; a[n_] := a[n] = Sum[EulerPhi[(n-1)/d]*a[d], {d, Divisors[n-1]}]; Table[a[n], {n, 1, 100}] (* Vaclav Kotesovec, Feb 23 2020 *)

Formula

a(1) = 1; a(n+1) = Sum_{d|n} phi(n/d) * a(d). - Ilya Gutkovskiy, Feb 23 2020