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A143525
a(n) is the number of divisors of (A005179(n)-1), where A005179(n) is the smallest positive integer with n divisors.
2
1, 2, 2, 4, 2, 6, 2, 4, 2, 8, 2, 24, 2, 4, 4, 16, 2, 32, 2, 6, 4, 16, 2, 8, 4, 4, 4, 64, 2, 96, 2, 8, 4, 4, 2, 512, 2, 4, 4, 192, 2, 144, 2, 4, 6, 16, 4, 16, 8, 8, 8, 128, 2, 12, 2, 16, 4, 64, 2, 4608, 4, 12, 2, 12, 8, 384, 4, 8, 2, 512, 2, 8192, 16, 4, 16, 8, 8, 192, 4, 8, 4, 32, 4, 24, 8
OFFSET
2,2
LINKS
FORMULA
a(n) = A000005(A005179(n)-1). - Ray Chandler, Oct 11 2008
PROG
(Python)
from math import prod
from sympy import isprime, divisors, divisor_count, prime
def A143525(n):
def mult_factors(n):
if isprime(n):
return [(n, )]
c = []
for d in divisors(n, generator=True):
if 1<d<n:
for a in mult_factors(n//d):
c.append(tuple(sorted((d, )+a)))
return list(set(c))
return int(divisor_count(min((prod(prime(i)**(j-1) for i, j in enumerate(reversed(d), 1)) for d in mult_factors(n)), default=1)-1)) # Chai Wah Wu, Aug 17 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Leroy Quet, Aug 22 2008
EXTENSIONS
Extended by Ray Chandler, Oct 11 2008
STATUS
approved