%I #18 Dec 10 2023 17:36:39
%S 1,2,3,0,5,1,7,0,0,3,11,1,13,5,2,0,17,1,19,3,4,9,23,1,0,11,0,5,29,3,
%T 31,0,8,15,2,1,37,17,10,3,41,5,43,9,2,21,47,1,0,3,14,11,53,1,6,5,16,
%U 27,59,3,61,29,4,0,8,9,67,15,20,5,71,1,73,35,2,17,4,11,79,3,0,39,83
%N a(n) = n if n is prime, a(n) = 0 if n is a nontrivial power of a prime, and otherwise a(n) = max{|p-q| where p, q are distinct primes dividing n}.
%F a(n) = A006530(n)-A020639(n) for n composite. - _Chai Wah Wu_, Jul 01 2020
%e a(12) = 1 because its prime factors (2x2x3) have a maximum difference of 1 (3-2).
%e a(14) = 5 because its prime factors (2x7) have a maximum difference of 5 (7-2).
%o (Python)
%o import numpy as np
%o def primeFactors(n):
%o x=[]
%o while n % 2 == 0:
%o x.append(2),
%o n = n / 2
%o for i in range(3,int(np.sqrt(n))+1,2):
%o while n % i== 0:
%o x.append(i),
%o n = n / i
%o if n > 2:
%o x.append(n)
%o if len(x)==0:
%o x.append(1)
%o if len(x)!=1:
%o y=x[-1]-x[0]
%o else:
%o y=x[0]
%o return y
%o print(len(x))
%o nums = list(range(1,101))
%o final=[]
%o for i in nums:
%o final.append(primeFactors(i))
%o final = [int(i) for i in final]
%o print(final)
%o (Python)
%o from sympy import primefactors, isprime
%o def A335940(n):
%o if isprime(n):
%o return n
%o else:
%o pf = primefactors(n)
%o return max(pf)-min(pf) # _Chai Wah Wu_, Jul 01 2020
%Y Cf. A006530, A020639.
%K nonn
%O 1,2
%A _Elam Blackwell_, Jun 30 2020
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