login
Position of first occurrence of n in A238529 (Recursive depth of n modulo sopfr(n)).
2

%I #36 May 10 2021 06:01:48

%S 2,8,22,166,778,4962,29922,179682,688078,7060198,42361338,674524645

%N Position of first occurrence of n in A238529 (Recursive depth of n modulo sopfr(n)).

%e The depth of 22 is 3 because 22->9->3, that is, 22 mod (11 + 2) = 9, 9 mod (3 + 3) = 3, and 3 mod (3) = 0, and 22 is the smallest number to have a depth of 3.

%e a(10) = 7060198, because 7060198->3530097->392185->78417->8665->1713->565->93->25->5

%o (Python)

%o def primfacs(n):

%o i = 2

%o primfacs = []

%o while i * i <= n:

%o while n % i == 0:

%o primfacs.append(i)

%o n = n / i

%o i = i + 1

%o if n > 1:

%o primfacs.append(n)

%o return primfacs

%o def sopfr(n):

%o plist = list(primfacs(n))

%o l = len(plist)

%o s = 0

%o while l > 0:

%o s += plist[l - 1]

%o l -= 1

%o return s

%o def sd(n):

%o d = 1

%o s = n % sopfr(n)

%o if s > 1:

%o d += sd(s)

%o return d

%o n=2

%o max=1000

%o rec = 0

%o lst = []

%o while n <= max:

%o r = sd(n)

%o if r > rec:

%o lst.append(n)

%o rec = r

%o n += 1

%o print(lst)

%K nonn,more

%O 1,1

%A _J. Stauduhar_, Feb 28 2014

%E a(12) from _Michel Marcus_, Mar 26 2014