The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A258650 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A258650

Tenth arithmetic derivative of n.
(history; published version)

#11 by Michel Marcus at Thu Nov 03 11:24:45 EDT 2022

STATUS

reviewed

approved

#10 by Joerg Arndt at Thu Nov 03 11:14:45 EDT 2022

STATUS

proposed

reviewed

#9 by Chai Wah Wu at Thu Nov 03 11:12:17 EDT 2022

STATUS

editing

proposed

#8 by Chai Wah Wu at Thu Nov 03 11:12:05 EDT 2022

PROG

if n <= 1: return 0

n = sum((n*e//p for p, e in factorint(n).items())) if n > 1 else 0

STATUS

proposed

editing

#7 by Chai Wah Wu at Thu Nov 03 11:07:13 EDT 2022

STATUS

editing

proposed

#6 by Chai Wah Wu at Thu Nov 03 11:07:06 EDT 2022

PROG

return n # Chai Wah Wu, Nov 03 2022

#5 by Chai Wah Wu at Thu Nov 03 11:06:56 EDT 2022

PROG

(Python)

from sympy import factorint

def A258650(n):

for _ in range(10):

n = sum((n*e//p for p, e in factorint(n).items())) if n > 1 else 0

return n # Chai Wah Wu, Nov 03 2022

STATUS

approved

editing

#4 by Alois P. Heinz at Sat Jun 06 20:26:01 EDT 2015

STATUS

editing

approved

#3 by Alois P. Heinz at Sat Jun 06 20:25:29 EDT 2015

LINKS

Alois P. Heinz, <a href="/A258650/b258650.txt">Table of n, a(n) for n = 0..10000</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:= n-> A(n, 10):

seq(a(n), n=0..70);

#2 by Alois P. Heinz at Sat Jun 06 20:21:19 EDT 2015

NAME

allocated for Alois P. Heinz

Tenth arithmetic derivative of n.

DATA

0, 0, 0, 0, 4, 0, 0, 0, 8592, 0, 0, 0, 20096, 0, 0, 3424, 70464, 0, 0, 0, 16304, 0, 0, 0, 32624, 0, 1520, 27, 70464, 0, 0, 0, 235072, 0, 0, 8592, 47872, 0, 0, 20096, 24640, 0, 0, 0, 65264, 8592, 0, 0, 130544, 0, 3424, 8144, 47872, 0, 57996, 20096, 198656, 0, 0

OFFSET

0,5

FORMULA

a(n) = A003415^10(n).

CROSSREFS

Column k=10 of A258651.

Cf. A003415.

KEYWORD

allocated

nonn

AUTHOR

Alois P. Heinz, Jun 06 2015

STATUS

approved

editing