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Revision History for A001371 (Bold, blue-underlined text is an addition; faded, red-underlined text is a deletion.)

Showing entries 1-10 | older changes
Number of n-bead necklaces with beads of 2 colors and primitive period n, when turning over is allowed.
(history; published version)
#65 by N. J. A. Sloane at Fri Feb 03 16:31:59 EST 2023
STATUS

proposed

approved

#64 by Michael De Vlieger at Fri Feb 03 12:30:28 EST 2023
STATUS

editing

proposed

#63 by Michael De Vlieger at Fri Feb 03 12:30:26 EST 2023
LINKS

Jairo Bochi and Piotr Laskawiec, <a href="https://arxiv.org/abs/2301.12574">Spectrum maximizing products are not generically unique</a>, arXiv:2301.12574 [math.OC], 2023.

STATUS

approved

editing

#62 by Peter Luschny at Thu Mar 25 10:23:37 EDT 2021
STATUS

reviewed

approved

#61 by Michel Marcus at Thu Mar 25 09:41:42 EDT 2021
STATUS

proposed

reviewed

#60 by F. Chapoton at Thu Mar 25 09:26:10 EDT 2021
STATUS

editing

proposed

Discussion
Thu Mar 25
09:41
Michel Marcus: yes, thanks
#59 by F. Chapoton at Thu Mar 25 09:26:03 EDT 2021
PROG

return 1 if n<1 else ((2**(n//2+1) if n%2 + else 3)/4*2**(n//2-1)) + sum(totient(n//d)*2**d for d in divisors(n))/(2*/n)//2

STATUS

proposed

editing

Discussion
Thu Mar 25
09:26
F. Chapoton: fixed py3 code
#58 by F. Chapoton at Thu Mar 25 09:06:02 EDT 2021
STATUS

editing

proposed

Discussion
Thu Mar 25
09:09
Michel Marcus: output gives 1, 2.00000000000000, 1.00000000000000, 2.00000000000000, 3.00000000000000 ; can we have int's ?
09:18
F. Chapoton: problem already in A000029
#57 by F. Chapoton at Thu Mar 25 09:05:55 EDT 2021
PROG

def a000029(n):

def a000029(n): return 1 if n<1 else (n%2 + 3)/4*2**int(n//2) + sum([totient(n//d)*2**d for d in divisors(n)])/(2*n)

def a(n):

def a(n): return 1 if n<1 else sum([mobius(d)*a000029(n//d) for d in divisors(n)])

print ([a(n) for n in range(51)] ) # Indranil Ghosh, Apr 23 2017

STATUS

approved

editing

Discussion
Thu Mar 25
09:06
F. Chapoton: adapt py code to py3
#56 by N. J. A. Sloane at Sat Dec 07 12:18:17 EST 2019
PROG

print [a(n) for n in xrangerange(51)] # Indranil Ghosh, Apr 23 2017

Discussion
Sat Dec 07
12:18
OEIS Server: https://oeis.org/edit/global/2837