The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A060992

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A060992

a(n) = Sum_{gcd(i,j) | 0 < i <= j < n and i+j = n}.
(history; published version)

#29 by Alois P. Heinz at Wed Oct 24 17:21:05 EDT 2018

STATUS

proposed

approved

#28 by Ilya Gutkovskiy at Wed Oct 24 15:04:30 EDT 2018

STATUS

editing

proposed

#27 by Ilya Gutkovskiy at Wed Oct 24 14:12:12 EDT 2018

FORMULA

G.f.: Sum_{k>=1} phi(k)*x^(2*k)/((1 + x^k)*(1 - x^k)^2). - Ilya Gutkovskiy, Oct 24 2018

STATUS

approved

editing

#26 by Peter Luschny at Fri May 11 06:09:59 EDT 2018

STATUS

reviewed

approved

#25 by Joerg Arndt at Fri May 11 03:09:23 EDT 2018

STATUS

proposed

reviewed

#24 by Michel Marcus at Fri May 11 02:43:41 EDT 2018

STATUS

editing

proposed

#23 by Michel Marcus at Fri May 11 02:43:27 EDT 2018

PROG

(PARI) a(n) = sumdiv(n, d, (d\2)*eulerphi(n/d)); \\ Michel Marcus, May 11 2018

STATUS

proposed

editing

#22 by Robert Israel at Fri May 11 02:23:19 EDT 2018

STATUS

editing

proposed

Discussion

Fri May 11

02:35

Michel Marcus: 1st formula : a(n) = Sum_{d divides n} floor(d/2)*phi(n/d) does not give the terms for me

02:43

Michel Marcus: no, my mistake

#21 by Robert Israel at Fri May 11 02:03:52 EDT 2018

KEYWORD

nonn,easy,changed,look

#20 by Robert Israel at Fri May 11 02:03:09 EDT 2018

LINKS

Robert Israel, <a href="/A060992/b060992.txt">Table of n, a(n) for n = 1..10000</a>

MAPLE

N:= 200: # to get a(1)..a(N)

A:= Vector(N):

for d from 1 to N do

c:= floor(d/2);

for n from d to N by d do

A[n]:= A[n]+c*numtheory:-phi(n/d)

od

od:

seq(A[i], i=1..N); # Robert Israel, May 11 2018

STATUS

approved

editing