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A351126
a(n) = A195199(n) / n.
1
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
1,1
COMMENTS
a(n) = 4 for all odd n. For all even n, a(n) >= 6.
LINKS
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 *)
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
J. Lowell, Feb 03 2022
STATUS
approved