login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A365400 a(n) = 64 + A000720(n) - A365339(n). 10
63, 63, 63, 62, 62, 62, 62, 62, 61, 61, 61, 61, 61, 61, 60, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 58, 58, 58, 58, 58, 58, 58, 58, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 56 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
It is conjectured that A365339(n) = PrimePi(n) + 64 for all n >= 31957 (Pollack et al.). Assuming this conjecture a(n) = 0 for n > 31956.
a is not monotonically decreasing.
LINKS
Paul Pollack, Carl Pomerance, and Enrique Treviño, Sets of monotonicity for Euler's totient function, preprint. See M(n).
Paul Pollack, Carl Pomerance, and Enrique Treviño, Sets of monotonicity for Euler's totient function, Ramanujan J. 30 (2013), no. 3, pp. 379-398.
Terence Tao, Monotone non-decreasing sequences of the Euler totient function, arXiv:2309.02325 [math.NT], 2023.
PROG
(Julia) # Computes the first N terms of the sequence.
using Nemo
function A365400List(N)
phi = Int64[i for i in 1:N + 1]
for i in 2:N + 1
if phi[i] == i
for j in i:i:N + 1
phi[j] -= div(phi[j], i)
end end end
lst = zeros(Int64, N)
dyn = zeros(Int64, N)
pi = 64
for n in 1:N
p = phi[n]
nxt = dyn[p] + 1
while p <= N && dyn[p] < nxt
dyn[p] = nxt
p += 1
end
pi += is_prime(n) ? 1 : 0
lst[n] = pi - dyn[n]
end
return lst
end
println(A365400List(32000))
(Python)
from bisect import bisect
from sympy import totient, primepi
def A365400(n):
plist, qlist, c = tuple(totient(i) for i in range(1, n+1)), [0]*(n+1), 0
for i in range(n):
qlist[a:=bisect(qlist, plist[i], lo=1, hi=c+1, key=lambda x:plist[x])]=i
c = max(c, a)
return 64+primepi(n)-c # Chai Wah Wu, Sep 06 2023
CROSSREFS
Sequence in context: A086859 A278827 A125638 * A365397 A332926 A112816
KEYWORD
nonn
AUTHOR
Peter Luschny, Sep 06 2023
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 3 07:55 EST 2024. Contains 370499 sequences. (Running on oeis4.)