The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A068238 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A068238

Denominators of arithmetic derivative of 1/n: -A003415(n)/n^2.
(history; published version)

#15 by Michael De Vlieger at Thu Nov 03 16:35:52 EDT 2022

STATUS

reviewed

approved

#14 by Michel Marcus at Thu Nov 03 12:07:18 EDT 2022

STATUS

proposed

reviewed

#13 by Chai Wah Wu at Thu Nov 03 11:57:22 EDT 2022

STATUS

editing

proposed

#12 by Chai Wah Wu at Thu Nov 03 11:57:19 EDT 2022

PROG

(Python)

from fractions import Fraction

from sympy import factorint

def A068238(n): return Fraction(sum((Fraction(e, p) for p, e in factorint(n).items())), n).denominator # Chai Wah Wu, Nov 03 2022

STATUS

approved

editing

#11 by Susanna Cuyler at Tue Mar 12 09:20:28 EDT 2019

STATUS

proposed

approved

#10 by Michel Marcus at Tue Mar 12 08:59:05 EDT 2019

STATUS

editing

proposed

#9 by Michel Marcus at Tue Mar 12 08:58:58 EDT 2019

NAME

Denominators of arithmetic derivative of 1/n: -A003415(n)/n^2; numerators: A068237.

CROSSREFS

Cf. A003415, A068237 (numerators).

STATUS

proposed

editing

#8 by Jean-François Alcover at Tue Mar 12 08:48:56 EDT 2019

STATUS

editing

proposed

#7 by Jean-François Alcover at Tue Mar 12 08:48:53 EDT 2019

MATHEMATICA

d[n_] := If[n < 2, 0, n Sum[f[[2]]/f[[1]], {f, FactorInteger[n]}]];

a[n_] := Denominator[-d[n]/n^2];

Array[a, 80] (* Jean-François Alcover, Mar 12 2019 *)

STATUS

approved

editing

#6 by Alois P. Heinz at Sun Jun 07 09:17:28 EDT 2015

STATUS

editing

approved