A371695 -id:A371695 - cp's OEIS frontend

A372384 The smallest composite number k such that the digits of k and its prime factors, both written in base n, contain the same set of distinct digits.

4, 8, 30, 25, 57, 16, 27, 192, 132, 121, 185, 169, 465, 32, 306, 289, 489, 361, 451, 2250, 552, 529, 125, 1586, 81, 1652, 985, 841, 1057, 64, 1285, 86166, 2555, 1332, 1387, 1369, 4752, 3240, 2005, 1681, 2649, 1849, 2047, 5456, 2256, 2209, 343, 5050, 2761, 5876, 2862, 2809, 3097, 15512

Offset: 2

Scott R. Shannon, Apr 29 2024

			a(4) = 30 as 30 = 2 * 3 * 5 = 132_4 = 2_4 * 3_4 * 11_4, and both 132_4 and its prime factors contain the same distinct digits 1, 2, and 3.
a(10) = 132 as 132 = 2 * 3 * 11, and both 132 and its prime factors contain the same distinct digits 1, 2, and 3. See also A035141.
a(14) = 465 as 465 = 3 * 5 * 31 = 253_14 = 3_14 * 5_14 * 23_14, and both 253_14 and its prime factors contain the same distinct digits 2, 3, and 5.

Scott R. Shannon, Table of n, a(n) for n = 2..404

Cf. A027746, A035141, A035140, A372309, A371695, A000668.

a(n) = 2*n + 2 if n = 2^k - 1 with k >= 2, otherwise a(n) = n^2 if n is prime.

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

Original entry on oeis.org

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

Offset: 1

Scott R. Shannon, Apr 17 2024

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

			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.

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

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 *)

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

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

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A372384 The smallest composite number k such that the digits of k and its prime factors, both written in base n, contain the same set of distinct digits.

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

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