A238529 -id:A238529 - cp's OEIS frontend

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

J. Stauduhar, Feb 28 2014

			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

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)

a(12) from Michel Marcus, Mar 26 2014

A238714 Final divisor of A238529(n).

Original entry on oeis.org

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

J. Stauduhar, Mar 03 2014

nonn

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

			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.

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

Cf. A238529.

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)

A238525 n modulo sopfr(n), where sopfr(n) is the sum of the prime factors of n, with multiplicity.

Original entry on oeis.org

0, 0, 0, 0, 1, 0, 2, 3, 3, 0, 5, 0, 5, 7, 0, 0, 2, 0, 2, 1, 9, 0, 6, 5, 11, 0, 6, 0, 0, 0, 2, 5, 15, 11, 6, 0, 17, 7, 7, 0, 6, 0, 14, 1, 21, 0, 4, 7, 2, 11, 1, 0, 10, 7, 4, 13, 27, 0, 0, 0, 29, 11, 4, 11, 2, 0, 5, 17, 0, 0, 0, 0, 35, 10, 7, 5, 6, 0, 2, 9, 39

Offset: 2

J. Stauduhar, Feb 28 2014

a(A036844(n)) = 0. - Reinhard Zumkeller, Jul 21 2014

			a(6) = 1, because 6 mod sopfr(6) = 6 mod 5 = 1.

Reinhard Zumkeller, Table of n, a(n) for n = 2..10000

Cf. A001414, A238526, A238527, A238528, A238529, A238530.

Cf. A036844.

a238525 n = mod n $ a001414 n  -- Reinhard Zumkeller, Jul 21 2014

Table[Mod[n, Apply[Dot, Transpose[FactorInteger[n]]]], {n, 105}] (* Wouter Meeussen, Mar 01 2014 *)
mms[n_]:=Mod[n,Total[Flatten[Table[#[[1]],#[[2]]]&/@FactorInteger[ n]]]]; Array[mms,90,2] (* Harvey P. Dale, May 25 2016 *)

a(n) = n mod A001414(n).

A238621 Position of first occurrence of n in A238525.

Original entry on oeis.org

1, 6, 8, 9, 48, 12, 24, 15, 120, 22, 54, 26, 90, 57, 44, 34, 156, 38, 114, 85, 228, 46, 232, 87, 348, 93, 138, 58, 318, 62, 372, 111, 333, 265, 354, 74, 366, 129, 296, 82, 369, 86, 402, 667, 387, 94, 328, 159, 438, 244, 530, 106, 423, 177, 474, 183, 1416, 118, 498, 122, 742, 201, 590, 415, 534, 134, 610, 219

Offset: 0

Robert G. Wilson v, Mar 01 2014

Robert G. Wilson v, Table of n, a(n) for n = 0..1000

Cf. A238525, A238526, A238527, A238528, A238529.

f[n_] := Mod[n, Dot @@ Transpose@ FactorInteger@ n]; t = Table[0, {1000}]; k = 1; While[k < 100001, a = f[k]; If[a < 1001 && t[[a]] == 0, t[[a]] = k; Print[{a, k}]]; k++]; t

cp's OEIS Frontend

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

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A238714 Final divisor of A238529(n).

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A238525 n modulo sopfr(n), where sopfr(n) is the sum of the prime factors of n, with multiplicity.

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A238621 Position of first occurrence of n in A238525.

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