The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A046657 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A046657

a(n) = A002088(n)/2.
(history; published version)

#40 by Susanna Cuyler at Fri Mar 26 08:44:25 EDT 2021

STATUS

proposed

approved

#39 by Chai Wah Wu at Thu Mar 25 22:24:39 EDT 2021

STATUS

editing

proposed

#38 by Chai Wah Wu at Thu Mar 25 22:24:34 EDT 2021

PROG

return (n*(n-1)-c+j)//4 # Chai Wah Wu, Mar 25 2021

#37 by Chai Wah Wu at Thu Mar 25 22:24:21 EDT 2021

PROG

(Python)

from functools import lru_cache

@lru_cache(maxsize=None)

def A046657(n): # based on second formula in A018805

if n == 0:

return 0

c, j = 0, 2

k1 = n//j

while k1 > 1:

j2 = n//k1 + 1

c += (j2-j)*(4*A046657(k1)-1)

j, k1 = j2, n//j2

return (n*(n-1)-c+j)//4 # Chai Wah Wu, Mar 25 2021

STATUS

approved

editing

#36 by Bruno Berselli at Tue Mar 13 13:10:14 EDT 2018

STATUS

reviewed

approved

#35 by Michel Marcus at Tue Mar 13 13:06:23 EDT 2018

STATUS

proposed

reviewed

#34 by Muniru A Asiru at Mon Mar 05 10:10:48 EST 2018

STATUS

editing

proposed

Discussion

Tue Mar 13

13:06

Michel Marcus: formula, yes for me

#33 by Muniru A Asiru at Mon Mar 05 10:10:21 EST 2018

PROG

(GAP) List([12..60], n->Sum([1..n], k->Phi(k)/2)); # Muniru A Asiru, Mar 05 2018

#32 by Muniru A Asiru at Mon Mar 05 10:08:41 EST 2018

MAPLE

a:=n->sum(numtheory[phi](k), k=1..n): seq(a(n)/2, n=2..60); # Muniru A Asiru, Mar 05 2018

PROG

(GAP) List([1..60], n->Sum([1..n], k->Phi(k)/2)); # Muniru A Asiru, Mar 05 2018

STATUS

proposed

editing

#31 by Altug Alkan at Sun Mar 04 05:28:31 EST 2018

STATUS

editing

proposed