cp's OEIS Frontend

A258171 a(n) = Sum_{d|n} phi(d)*Bell(n/d) for n>0, a(0) = 0.

%I A258171 #24 May 09 2021 08:08:53
%S A258171 0,1,3,7,19,56,214,883,4163,21163,116039,678580,4213848,27644449,
%T A258171 190900217,1382958677,10480146333,82864869820,682076827740,
%U A258171 5832742205075,51724158351527,474869816158547,4506715739125923,44152005855084368,445958869299027638
%N A258171 a(n) = Sum_{d|n} phi(d)*Bell(n/d) for n>0, a(0) = 0.
%C A258171 Dirichlet convolution of phi(n) (A000010) and the Bell numbers (A000110) (n >= 1). - _Richard L. Ollerton_, May 09 2021
%H A258171 Alois P. Heinz, <a href="/A258171/b258171.txt">Table of n, a(n) for n = 0..500</a>
%F A258171 a(n) = Sum_{k=0..n} A258170(n,k).
%F A258171 For n >= 1, a(n) = Sum_{k=1..n} Bell(gcd(n,k)). - _Richard L. Ollerton_, May 09 2021
%p A258171 with(numtheory):
%p A258171 A:= proc(n, k) option remember;
%p A258171       add(phi(d)*k^(n/d), d=divisors(n))
%p A258171     end:
%p A258171 T:= (n, k)-> add((-1)^(k-i)*binomial(k, i)*A(n, i), i=0..k)/k!:
%p A258171 a:= n-> add(T(n, k), k=0..n):
%p A258171 seq(a(n), n=0..30);
%t A258171 a[n_] := If[n == 0, 0, DivisorSum[n, EulerPhi[#] BellB[n/#] &]];
%t A258171 Table[a[n], {n, 0, 25}] (* _Peter Luschny_, Aug 27 2019 *)
%Y A258171 Row sums of A258170.
%Y A258171 Similar: A078392 (numbpart), this sequence (bell), A053635 (numbcomb), A181847 and A034738 (numbcomp), A327030 (numbperm).
%Y A258171 Cf. A000010, A000110.
%K A258171 nonn
%O A258171 0,3
%A A258171 _Alois P. Heinz_, May 22 2015
%E A258171 New name from _Peter Luschny_, Aug 27 2019