A143525 - OEIS

%I #17 Aug 17 2024 22:29:43

%S 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,

%T 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,

%U 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

%N a(n) is the number of divisors of (A005179(n)-1), where A005179(n) is the smallest positive integer with n divisors.

%H Amiram Eldar, <a href="/A143525/b143525.txt">Table of n, a(n) for n = 2..1000</a>

%F a(n) = A000005(A005179(n)-1). - _Ray Chandler_, Oct 11 2008

%o (Python)

%o from math import prod

%o from sympy import isprime, divisors, divisor_count, prime

%o def A143525(n):

%o     def mult_factors(n):

%o         if isprime(n):

%o             return [(n,)]

%o         c = []

%o         for d in divisors(n,generator=True):

%o             if 1<d<n:

%o                 for a in mult_factors(n//d):

%o                     c.append(tuple(sorted((d,)+a)))

%o         return list(set(c))

%o     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

%Y Cf. A000005, A005179, A143526.

%K nonn

%O 2,2

%A _Leroy Quet_, Aug 22 2008

%E Extended by _Ray Chandler_, Oct 11 2008