A371696 Composite numbers that divide the reverse of the concatenation of their ascending order prime factors, with repetition.

26, 38, 46, 378, 26579, 84941, 178838, 30791466, 39373022, 56405502, 227501395, 904085931, 1657827142

Offset: 1

Author

Scott R. Shannon, Apr 03 2024

Keywords

• nonn
• base
• more

Comments

a(14) > 10^10, if it exists. - Daniel Suteu, Apr 28 2024

Examples

			26 is a term as 26 = 2 * 13 = "213" which is reverse is "312", and 312 is divisible by 26.
227501395 is a term as 227501395 = 5 * 11 * 17 * 23 * 71 * 149 = "511172371149" which in reverse is "941173271115", and 941173271115 is divisible by 227501395.
		

Crossrefs

Cf. A027746, A037276, A259047, A371641, A371666.

Programs

Python

from itertools import count, islice
from sympy import isprime, factorint
def ok(k): return not isprime(k) and int("".join(str(p)[::-1]*e for p, e in list(factorint(k).items())[::-1]))%k == 0
def agen(): yield from filter(ok, count(4))
print(list(islice(agen(), 7))) # Michael S. Branicky, Apr 13 2024

Python

from itertools import count, islice
from sympy import factorint
def A371696_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,reverse=True):
                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
A371696_list = list(islice(A371696_gen(),6)) # Chai Wah Wu, Apr 13 2024

Extensions

a(13) from Daniel Suteu, Apr 28 2024