A144818 - OEIS

%I #12 Dec 18 2020 18:45:23

%S 1,1,5,25,135,675,3475,17375,87385,437175,2188575,10942875,54730525,

%T 273652625,1368332625,6841676625,34208737630,171043688150,

%U 855220256700,4276101283500,21380515232550,106902576510250,534512926322750

%N Shifts left when Dirichlet convolution with a (DC:(b,a)->c) applied 4 times.

%H Alois P. Heinz, <a href="/A144818/b144818.txt">Table of n, a(n) for n = 1..1000</a>

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%p with(numtheory): dc:= proc(b,c) proc(n) option remember; add(b(d) *c(n/d), d=`if`(n<0,{},divisors(n))) end end: A:= proc(n, k) local a, b, t; b[1]:= dc(a,a); for t from 2 to k do b[t]:= dc(b[t-1],a) od: a:= n-> `if`(n=1, 1, b[k](n-1)); a(n) end: a:= n-> A(n,4): seq(a(n), n=1..30);

%t dc[b_, c_] := Module[{f}, f[n_] := f[n] = Sum[b[d] c[n/d], {d, If[n<0, {}, Divisors[n]]}]; f];

%t A[n_, k_] := Module[{a, b, t}, b[1] = dc[a, a]; For[t = 2, t <= k, t++, b[t] = dc[b[t-1], a]]; a = Function[m, If[m= 1, 1, b[k][m-1]]]; a[n]];

%t a[n_] := A[n, 4];

%t Array[a, 30] (* _Jean-François Alcover_, Dec 18 2020, after Maple *)

%Y 4th column of A144823.

%K eigen,nonn

%O 1,3

%A _Alois P. Heinz_, Sep 21 2008