A351126 a(n) = A195199(n) / n.

4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 10, 4, 6, 4, 6, 4, 8, 4, 6, 4, 6, 4, 10, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 10, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 10, 4, 6, 4, 6, 4, 8, 4, 6, 4, 6, 4, 12, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 10, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 10, 4

Offset: 1

Author

J. Lowell, Feb 03 2022

Keywords

• nonn

Comments

a(n) = 4 for all odd n. For all even n, a(n) >= 6.

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A195199, A337686.

Programs

Mathematica

a[n_] := Module[{d = DivisorSigma[0, n], k = 1}, While[DivisorSigma[0, k*n] <= 2*d, k++]; k]; Array[a, 100] (* Amiram Eldar, Feb 03 2022 *)

PARI

a(n) = my(m=n, d=numdiv(n)); while(numdiv(m)<=2*d, m+=n); m/n; \\ Michel Marcus, Feb 27 2022

Python

from math import prod
from collections import Counter
from itertools import count
from sympy import factorint
def A351126(n):
    f = Counter(factorint(n))
    d = prod(e+1 for e in f.values())
    for m in count(2):
        if prod(e+1 for e in (f+Counter(factorint(m))).values()) > 2*d:
            return m # Chai Wah Wu, Feb 28 2022