The On-Line Encyclopedia of Integer Sequences (OEIS)

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A258652

Sum of the k-th arithmetic derivative of n-k for k=0..n.
(history; published version)

#12 by Bruno Berselli at Fri Jun 01 04:04:42 EDT 2018

STATUS

reviewed

approved

#11 by Michel Marcus at Fri Jun 01 03:53:29 EDT 2018

STATUS

proposed

reviewed

#10 by Jean-François Alcover at Fri Jun 01 03:46:58 EDT 2018

STATUS

editing

proposed

#9 by Jean-François Alcover at Fri Jun 01 03:46:54 EDT 2018

MATHEMATICA

d[n_ /; n>1] := n*Sum[i[[2]]/i[[1]], {i, FactorInteger[n]}]; d[_] = 0;

A[n_, k_] := A[n, k] = If[k == 0, n, d[A[n, k-1]]];

a[n_] := a[n] = Sum[A[h, n-h], {h, 0, n}];

Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Jun 01 2018, from Maple *)

STATUS

approved

editing

#8 by Alois P. Heinz at Mon Feb 06 14:41:09 EST 2017

STATUS

editing

approved

#7 by Alois P. Heinz at Mon Feb 06 14:41:06 EST 2017

LINKS

Wikipedia, <a href="httphttps://en.wikipedia.org/wiki/Arithmetic_derivative">Arithmetic derivative</a>

STATUS

approved

editing

#6 by Alois P. Heinz at Sat Jun 06 21:34:14 EDT 2015

STATUS

editing

approved

#5 by Alois P. Heinz at Sat Jun 06 21:34:09 EDT 2015

LINKS

Wikipedia, <a href="http://en.wikipedia.org/wiki/Arithmetic_derivative">Arithmetic derivative</a>

#4 by Alois P. Heinz at Sat Jun 06 21:33:34 EDT 2015

LINKS

Alois P. Heinz, <a href="/A258652/b258652.txt">Table of n, a(n) for n = 0..100</a>

MAPLE

d:= n-> n*add(i[2]/i[1], i=ifactors(n)[2]):

A:= proc(n, k) option remember; `if`(k=0, n, d(A(n, k-1))) end:

a:= proc(n) option remember; add(A(h, n-h), h=0..n) end:

seq(a(n), n=0..40);

#3 by Alois P. Heinz at Sat Jun 06 20:56:22 EDT 2015

NAME

Sum of the k-th arithmetic derivatives derivative of n-k for k=0..n.