A355331 Numbers k that divide A020696(k).

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

Author

Amiram Eldar, Jun 29 2022

Keywords

• nonn

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.

Examples

			2 is a term since A020696(2) = 6 is divisible by 2.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A020696.

A355332 is a subsequence.

Programs

Mathematica

v[n_] := Times @@ (Divisors[n] + 1); Select[Range[1000], Divisible[v[#], #] &]

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