The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A318879

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A318879

a(n) = Sum_{d|n} [d-(2*phi(d)) > 0]*(d-(2*phi(d))).
(history; published version)

#10 by Susanna Cuyler at Wed Sep 05 17:18:24 EDT 2018

STATUS

proposed

approved

#9 by Antti Karttunen at Wed Sep 05 16:10:29 EDT 2018

STATUS

editing

proposed

#8 by Antti Karttunen at Wed Sep 05 16:08:45 EDT 2018

FORMULA

a(n) = -Sum_{d|n} [A083254(d) < 0]*A083254(d), where A083254(n) = 2*phi(n) - n, and [ ] are the Iverson brackets.

Discussion

Wed Sep 05

16:10

Antti Karttunen: Done.

#7 by Antti Karttunen at Wed Sep 05 16:03:38 EDT 2018

FORMULA

a(n) = -Sum_{d|n} [A083254(d) < 0]*A083254(d), where A083254(n) = 2*phi(n) - n, and [ ] are Iverson brackets.

STATUS

proposed

editing

#6 by Antti Karttunen at Wed Sep 05 10:13:38 EDT 2018

STATUS

editing

proposed

Discussion

Wed Sep 05

15:11

Peter Luschny: dito

#5 by Antti Karttunen at Wed Sep 05 10:04:41 EDT 2018

LINKS

Antti Karttunen, <a href="/A318879/b318879.txt">Table of n, a(n) for n = 1..65537</a>

#4 by Antti Karttunen at Wed Sep 05 10:00:48 EDT 2018

EXAMPLE

n = 105 has divisors [1, 3, 5, 7, 15, 21, 35, 105]. When A083254 is applied to them, we obtain [1, 1, 3, 5, 1, 3, 13, -9]. Summing the negative numbers present, and negating, we get a(105) = -(-9) = 9.

#3 by Antti Karttunen at Wed Sep 05 08:34:01 EDT 2018

FORMULA

a(n) = A318878(n) - A033879(n).

#2 by Antti Karttunen at Wed Sep 05 08:18:39 EDT 2018

NAME

allocated for Antti Karttunen

a(n) = Sum_{d|n} [d-(2*phi(d)) > 0]*(d-(2*phi(d))).

DATA

0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 6, 0, 2, 0, 0, 0, 8, 0, 6, 0, 2, 0, 14, 0, 2, 0, 6, 0, 18, 0, 0, 0, 2, 0, 24, 0, 2, 0, 14, 0, 22, 0, 6, 0, 2, 0, 30, 0, 12, 0, 6, 0, 26, 0, 14, 0, 2, 0, 54, 0, 2, 0, 0, 0, 30, 0, 6, 0, 26, 0, 56, 0, 2, 0, 6, 0, 34, 0, 30, 0, 2, 0, 66, 0, 2, 0, 14, 0, 66, 0, 6, 0, 2, 0, 62, 0, 16, 0, 36, 0, 42, 0, 14, 9

OFFSET

1,6

FORMULA

a(n) = -Sum_{d|n} [A083254(d) < 0]*A083254(d), where A083254(n) = 2*phi(n) - n.

PROG

(PARI) A318879(n) = sumdiv(n, d, d=d-(2*eulerphi(d)); (d>0)*d);

CROSSREFS

Cf. A000010, A033879, A083254, A318878.

Cf. also A318679.

KEYWORD

allocated

nonn

AUTHOR

Antti Karttunen, Sep 05 2018

STATUS

approved

editing

#1 by Antti Karttunen at Wed Sep 05 07:52:25 EDT 2018

NAME

allocated for Antti Karttunen

KEYWORD

allocated

STATUS

approved