The On-Line Encyclopedia of Integer Sequences® (OEIS®)

Revision History for A300251

(Underlined text is an addition; strikethrough text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A300251

Möbius transform of arithmetic derivative (A003415).
(history; published version)

#11 by Joerg Arndt at Wed Mar 14 03:48:50 EDT 2018

STATUS

reviewed

approved

#10 by Michel Marcus at Wed Mar 14 02:39:02 EDT 2018

STATUS

proposed

reviewed

#9 by Jon E. Schoenfield at Tue Mar 13 23:17:52 EDT 2018

STATUS

editing

proposed

#8 by Jon E. Schoenfield at Tue Mar 13 23:17:50 EDT 2018

NAME

Möbius- transform of arithmetic derivative (A003415).

STATUS

approved

editing

#7 by Susanna Cuyler at Thu Mar 08 21:19:57 EST 2018

STATUS

proposed

approved

#6 by Antti Karttunen at Thu Mar 08 11:50:40 EST 2018

STATUS

editing

proposed

#5 by Antti Karttunen at Thu Mar 08 11:48:57 EST 2018

CROSSREFS

#4 by Antti Karttunen at Thu Mar 08 10:28:31 EST 2018

LINKS

Antti Karttunen, <a href="/A300251/b300251.txt">Table of n, a(n) for n = 1..65537</a>

#3 by Antti Karttunen at Thu Mar 08 10:10:44 EST 2018

	NAME	`MoebiusMöbius-transform of arithmetic derivative (A003415).`
	FORMULA	`a(n) = A003415(n) - A300252(n).`
	CROSSREFS	`Cf. A003415, A008683, A300252, A300253.`

#2 by Antti Karttunen at Thu Mar 08 09:46:49 EST 2018

	NAME	`allocatedMoebius-transform forof Anttiarithmetic Karttunenderivative (A003415).`
	DATA	`0, 1, 1, 3, 1, 3, 1, 8, 5, 5, 1, 8, 1, 7, 6, 20, 1, 11, 1, 14, 8, 11, 1, 20, 9, 13, 21, 20, 1, 14, 1, 48, 12, 17, 10, 28, 1, 19, 14, 36, 1, 20, 1, 32, 26, 23, 1, 48, 13, 29, 18, 38, 1, 39, 14, 52, 20, 29, 1, 36, 1, 31, 36, 112, 16, 32, 1, 50, 24, 34, 1, 68, 1, 37, 38, 56, 16, 38, 1, 88, 81, 41, 1, 52, 20, 43, 30, 84, 1, 50`
	OFFSET	`1,4`
	FORMULA	`a(n) = Sum_{d\|n} A008683(n/d)*A003415(d).`
	PROG	`(PARI)` `A003415(n) = {my(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], nfac[i, 2]/fac[i, 1]))}; \\ From A003415` `A300251(n) = sumdiv(n, d, moebius(n/d)A003415(d));`
	CROSSREFS	`Cf. A003415, A008683, A300252.`
	KEYWORD	`allocated` `nonn`
	AUTHOR	`Antti Karttunen, Mar 08 2018`
	STATUS	`approved` `editing`

Last modified August 18 19:26 EDT 2024. Contains 375273 sequences. (Running on oeis4.)