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A258171 a(n) = Sum_{d|n} phi(d)*Bell(n/d) for n>0, a(0) = 0. 3
0, 1, 3, 7, 19, 56, 214, 883, 4163, 21163, 116039, 678580, 4213848, 27644449, 190900217, 1382958677, 10480146333, 82864869820, 682076827740, 5832742205075, 51724158351527, 474869816158547, 4506715739125923, 44152005855084368, 445958869299027638 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..500

FORMULA

a(n) = Sum_{k=0..n} A258170(n,k).

MAPLE

with(numtheory):

A:= proc(n, k) option remember;

      add(phi(d)*k^(n/d), d=divisors(n))

    end:

T:= (n, k)-> add((-1)^(k-i)*binomial(k, i)*A(n, i), i=0..k)/k!:

a:= n-> add(T(n, k), k=0..n):

seq(a(n), n=0..30);

MATHEMATICA

a[n_] := If[n == 0, 0, DivisorSum[n, EulerPhi[#] BellB[n/#] &]];

Table[a[n], {n, 0, 25}] (* Peter Luschny, Aug 27 2019 *)

CROSSREFS

Row sums of A258170.

Similar: A078392 (numbpart), this sequence (bell), A053635 (numbcomb), A181847 and A034738 (numbcomp), A327030 (numbperm).

Cf. A000010, A000110.

Sequence in context: A071716 A306088 A188625 * A263334 A005506 A268125

Adjacent sequences:  A258168 A258169 A258170 * A258172 A258173 A258174

KEYWORD

nonn

AUTHOR

Alois P. Heinz, May 22 2015

EXTENSIONS

New name from Peter Luschny, Aug 27 2019

STATUS

approved

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Last modified October 22 14:44 EDT 2019. Contains 328318 sequences. (Running on oeis4.)