A309633 - OEIS

%I #12 Jan 22 2025 11:59:45

%S 0,1,1,1,2,1,3,1,3,2,4,1,5,1,5,6,4,1,7,1,13,11,6,1,7,17,7,11,31,1,45,

%T 1,10,18,6,146,34,1,9,27,141,1,261,1,78,364,8,1,44,730,537,18,145,1,

%U 255,1281,2203,51,33,1,2213,1,47,7461,221,4722,1159,1,85,38,27948,1,2342,1,36,17060,347,63146,3427,1

%N G.f.: x * Sum_{k>=1} x^k / (1 - a(k)*x^k).

%H Antti Karttunen, <a href="/A309633/b309633.txt">Table of n, a(n) for n = 1..14665</a>

%F a(1) = 0; a(n+1) = Sum_{d|n} a(d)^(n/d-1).

%t a[n_] := a[n] = SeriesCoefficient[x Sum[x^k/(1 - a[k] x^k), {k, 1, n - 1}], {x, 0, n}]; Table[a[n], {n, 1, 80}]

%t a[n_] := a[n] = Sum[a[d]^((n - 1)/d - 1) , {d, Divisors[n - 1]}]; a[1] = 0; a[2] = 1; Table[a[n], {n, 1, 80}]

%o (PARI) seq(n)={my(v=vector(n)); for(n=1, #v-1, v[n+1]=sumdiv(n, d, v[d]^(n/d-1))); v} \\ _Andrew Howroyd_, Aug 10 2019

%Y Cf. A028815 (positions of 1's), A087909, A127525, A309634.

%K nonn,changed

%O 1,5

%A _Ilya Gutkovskiy_, Aug 10 2019