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A355331
Numbers k that divide A020696(k).
2
1, 2, 6, 12, 20, 24, 42, 60, 72, 84, 90, 120, 126, 140, 144, 156, 168, 180, 210, 216, 220, 240, 252, 280, 312, 336, 342, 360, 420, 432, 440, 462, 468, 480, 504, 540, 560, 600, 624, 630, 660, 672, 684, 700, 720, 770, 780, 816, 840, 864, 880, 900, 924, 936, 945, 960, 990
OFFSET
1,2
COMMENTS
If k and m are coprime terms then k*m is also a term.
The least odd term above 1 is a(55) = 945, the least term above 1 that is coprime to 6 is a(378) = 10465, least term above 1 that is coprime to 30 is a(3122) = 151487, and the least term above 1 that is coprime to 210 is a(6858) = 414713.
LINKS
EXAMPLE
2 is a term since A020696(2) = 6 is divisible by 2.
MATHEMATICA
v[n_] := Times @@ (Divisors[n] + 1); Select[Range[1000], Divisible[v[#], #] &]
PROG
(PARI) f(n) = my(d = divisors(n)); prod(i=1, #d, d[i]+1); \\ A020696
isok(k) = !(f(k) % k); \\ Michel Marcus, Jun 30 2022
(Python)
from itertools import count, islice
from functools import reduce
from sympy import divisors
def A355331_gen(startvalue=1): # generator of terms >= startvalue
return filter(lambda n:reduce(lambda a, b:a*b%n, (d+1 for d in divisors(n, generator=True)))%n==0, count(max(startvalue, 1)))
A355331_list = list(islice(A355331_gen(), 30)) # Chai Wah Wu, Jun 30 2022
CROSSREFS
Cf. A020696.
A355332 is a subsequence.
Sequence in context: A141406 A045619 A028690 * A270878 A120344 A031426
KEYWORD
nonn
AUTHOR
Amiram Eldar, Jun 29 2022
STATUS
approved