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A238714 Final divisor of A238529(n).

%I A238714 #31 May 09 2021 11:17:51
%S A238714 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,
%T A238714 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,
%U A238714 59,12,61,29,11,4,11,2,67,5,17,14,71,12,73,11,3,7,5,5
%N A238714 Final divisor of A238529(n).
%C A238714 Conjecture:  Every integer greater than 1, except 6, is an element of the sequence.
%H A238714 Tom Davis, <a href="/A238714/b238714.txt">Table of n, a(n) for n = 2..10001</a>
%e A238714 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.
%e A238714 a(21) = 10, because 21 mod sopfr(21) = 21 mod 10 = 1, and 10 is the last divisor used.
%o A238714 (Python)
%o A238714 def primfacs(n):
%o A238714    i = 2
%o A238714    primfac = []
%o A238714    while i * i <= n:
%o A238714        while n % i == 0:
%o A238714            primfac.append(i)
%o A238714            n //= i
%o A238714        i += 1
%o A238714    if n > 1:
%o A238714        primfac.append(n)
%o A238714    return primfac
%o A238714 def sopfr(n):
%o A238714    plist = primfacs(n)
%o A238714    l = len(plist)
%o A238714    s = 0
%o A238714    while l > 0:
%o A238714        s += plist[l - 1]
%o A238714        l -= 1
%o A238714    return s
%o A238714 n = 2
%o A238714 max = 1000
%o A238714 lst = []
%o A238714 while n <= max:
%o A238714    rem = n
%o A238714    while rem > 1:
%o A238714        last = sopfr(rem)
%o A238714        rem = rem % last
%o A238714    lst.append(last)
%o A238714    n += 1
%o A238714 print(lst)
%Y A238714 Cf. A238529.
%K A238714 nonn
%O A238714 2,1
%A A238714 _J. Stauduhar_, Mar 03 2014