A238530 Position of first occurrence of n in A238529 (Recursive depth of n modulo sopfr(n)).

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

Offset: 1

Author

J. Stauduhar, Feb 28 2014

Keywords

• nonn
• more

Examples

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

Programs

Python

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

Extensions

a(12) from Michel Marcus, Mar 26 2014