A332792 a(1) = 1; a(n) = Sum_{d|n, d < n} phi(d) * a(d).

1, 1, 1, 2, 1, 4, 1, 6, 3, 6, 1, 16, 1, 8, 7, 30, 1, 30, 1, 34, 9, 12, 1, 104, 5, 14, 21, 60, 1, 96, 1, 270, 13, 18, 11, 278, 1, 20, 15, 330, 1, 174, 1, 136, 81, 24, 1, 1176, 7, 130, 19, 186, 1, 588, 15, 804, 21, 30, 1, 1204, 1, 32, 135, 4590, 17, 402, 1, 310, 25, 348

Offset: 1

Author

Ilya Gutkovskiy, Feb 24 2020

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A000010, A006874, A008578 (positions of 1's), A038045, A057660, A332791.

Programs

Mathematica

a[1] = 1; a[n_] := Sum[If[d < n, EulerPhi[d] a[d], 0], {d, Divisors[n]}]; Table[a[n], {n, 1, 70}]
a[1] = 1; a[n_] := a[n] = Sum[If[GCD[n, k] > 1, a[n/GCD[n, k]], 0], {k, 1, n}]; Table[a[n], {n, 1, 70}]

PARI

up_to = 20000;
A332792list(n) = { my(v=vector(n)); v[1] = 1; for(n=2, #v, v[n] = sumdiv(n, d, if(d==n, 0, v[d]*eulerphi(d)))); (v); };
v332792 = A332792list(up_to);
A332792(n) = v332792[n]; \\ Antti Karttunen, Jan 22 2025

Formula

a(1) = 1; a(n) = Sum_{k=1..n, gcd(n, k) > 1} a(n/gcd(n, k)).