A064649 Row sums of the table A047916.

1, 4, 12, 40, 140, 816, 5082, 40800, 363258, 3632880, 39916910, 479052528, 6227020956, 87178936992, 1307674429440, 20922800222848, 355687428096272, 6402373892575992, 121645100408832342, 2432902011892837920

Offset: 1

Author

Antti Karttunen, Oct 04 2001

Keywords

• nonn

Links

• Harry J. Smith, Table of n, a(n) for n=1..100

Crossrefs

Also n*A061417[n]. Cf. A047918, A002619.

Programs

Haskell

a064649 = sum . a047916_row  -- Reinhard Zumkeller, Mar 19 2014

Maple

A064649 := proc(n) local d, s; s := 0; for d in divisors(n) do s := s + phi(n/d)*(n/d)^d*d!; od; RETURN(s); end;

Mathematica

a[n_] := DivisorSum[n, EulerPhi[n/#]*(n/#)^#*#!&]; Array[a, 20] (* Jean-François Alcover, Mar 06 2016 *)

PARI

{ for (n=1, 100, a=0; v=divisors(n); for (i=1, length(v), d=v[i]; a+=eulerphi(n/d)*(n/d)^d*d!); write("b064649.txt", n, " ", a) ) } \\ Harry J. Smith, Sep 21 2009

PARI

a(n) = sumdiv(n, d, eulerphi(n/d)*(n/d)^d*d!); \\ Michel Marcus, Mar 06 2016

Formula

a(n) = Sum_{d|n} phi(n/d)*(n/d)^d*d!. - Michel Marcus, Mar 06 2016