A335940 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}.

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, 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, 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

Offset

1,2

Links

Table of n, a(n) for n=1..83.

Formula

a(n) = A006530(n)-A020639(n) for n composite. - Chai Wah Wu, Jul 01 2020

Example

a(12) = 1 because its prime factors (2x2x3) have a maximum difference of 1 (3-2).
a(14) = 5 because its prime factors (2x7) have a maximum difference of 5 (7-2).

Prog

(Python)
import numpy as np
def primeFactors(n):
    x=[]
    while n % 2 == 0:
        x.append(2),
        n = n / 2
    for i in range(3, int(np.sqrt(n))+1, 2):
        while n % i== 0:
            x.append(i),
            n = n / i
    if n > 2:
        x.append(n)
    if len(x)==0:
        x.append(1)
    if len(x)!=1:
        y=x[-1]-x[0]
    else:
        y=x[0]
    return y
    print(len(x))
nums = list(range(1, 101))
final=[]
for i in nums:
    final.append(primeFactors(i))
final = [int(i) for i in final]
print(final)
(Python)
from sympy import primefactors, isprime
def A335940(n):
    if isprime(n):
        return n
    else:
        pf = primefactors(n)
        return max(pf)-min(pf) # Chai Wah Wu, Jul 01 2020

Crossrefs

Cf. A006530, A020639.

Sequence in context: A066398 A138197 A140664 * A339767 A071321 A071322

Adjacent sequences: A335937 A335938 A335939 * A335941 A335942 A335943

Keyword

nonn

Author

Elam Blackwell, Jun 30 2020

Status

approved