A372046 Composite numbers that divide the concatenation of the reverse of their ascending order prime factors, with repetition.

998, 1636, 9998, 15584, 49447, 99998, 1639964, 2794612, 9999998, 15842836, 1639360636, 1968390098, 27879461212, 65226742928

Offset

1,1

Comments

A number 999...9998 will be a term if it has two prime factors 2 and 4999...999. Therefore 999999999999998 and 999...9998 (with 54 9's) are both terms. See A056712.

100000000000 < a(15) <= 999999999999998. Robert P. P. McKone, May 07 2024

Links

Table of n, a(n) for n=1..14.

Example

998 is a term as 998 = 2 * 499 = "2" * "994" when each prime factor is reversed. This gives "2994", and 2994 is divisible by 998.
15584 is a term as 15584 = 2 * 2 * 2 * 2 * 2 * 487 = "2" * "2" * "2" * "2" * "2" * "784" when each prime factor is reversed. This gives "22222784", and 22222784 is divisible by 15584.

Mathematica

a[n_Integer] := Module[{f}, f = Flatten[ConstantArray @@@ FactorInteger[n]]; If[Length[f] < 2, Return[False]]; Mod[FromDigits[StringJoin[StringReverse[IntegerString[#, 10]] & /@ f], 10], n] == 0];
Select[Range[2, 10^5], a] (* Robert P. P. McKone, May 03 2024 *)

Prog

(Python)
from itertools import count, islice
from sympy import factorint
def A372046_gen(startvalue=4): # generator of terms >= startvalue
    for n in count(max(startvalue, 4)):
        f = factorint(n)
        if sum(f.values()) > 1:
            c = 0
            for p in sorted(f):
                a = pow(10, len(s:=str(p)), n)
                q = int(s[::-1])
                for _ in range(f[p]):
                    c = (c*a+q)%n
            if not c:
                yield n
A372046_list = list(islice(A372046_gen(), 5)) # Chai Wah Wu, Apr 24 2024

Crossrefs

Cf. A371696, A371695, A371641, A027746, A056712.

Sequence in context: A091365 A235165 A259505 * A317594 A226752 A043527

Adjacent sequences: A372043 A372044 A372045 * A372047 A372048 A372049

Keyword

nonn,base,more

Author

Scott R. Shannon, Apr 17 2024

Extensions

a(13)-a(14) from Robert P. P. McKone, May 05 2024

Status

approved