A238714 Final divisor of A238529(n).

2, 3, 4, 5, 5, 7, 2, 3, 3, 11, 5, 13, 5, 7, 8, 17, 2, 19, 2, 10, 3, 23, 5, 5, 11, 9, 5, 29, 10, 31, 2, 5, 7, 11, 5, 37, 17, 7, 7, 41, 5, 43, 5, 11, 10, 47, 4, 7, 2, 11, 17, 53, 3, 7, 4, 13, 9, 59, 12, 61, 29, 11, 4, 11, 2, 67, 5, 17, 14, 71, 12, 73, 11, 3, 7, 5, 5

Offset: 2

Author

J. Stauduhar, Mar 03 2014

Keywords

• nonn

Comments

Conjecture: Every integer greater than 1, except 6, is an element of the sequence.

Examples

			a(8) = 2, because 8 mod sopfr(8) = 8 mod 6 = 2, and 2 mod sopfr(2) = 2 mod 2 = 0, and 2 is the last divisor used.
a(21) = 10, because 21 mod sopfr(21) = 21 mod 10 = 1, and 10 is the last divisor used.
		

Links

• Tom Davis, Table of n, a(n) for n = 2..10001

Crossrefs

Cf. A238529.

Programs

Python

def primfacs(n):
   i = 2
   primfac = []
   while i * i <= n:
       while n % i == 0:
           primfac.append(i)
           n //= i
       i += 1
   if n > 1:
       primfac.append(n)
   return primfac
def sopfr(n):
   plist = primfacs(n)
   l = len(plist)
   s = 0
   while l > 0:
       s += plist[l - 1]
       l -= 1
   return s
n = 2
max = 1000
lst = []
while n <= max:
   rem = n
   while rem > 1:
       last = sopfr(rem)
       rem = rem % last
   lst.append(last)
   n += 1
print(lst)