A308533 Numbers such that the sum of anti-divisors divides the concatenation (in ascending order) of anti-divisors.

3, 4, 6, 15, 27, 30, 54, 69, 90, 96, 99, 120, 126, 481, 564, 1050, 1656, 3480, 7680, 9612, 11520, 393216, 612846, 2220864, 5506086, 5579652, 8177664, 18087936, 23711514, 111544794, 440477976, 555176025

Offset: 1

Author

Paolo P. Lava, Jun 06 2019

Keywords

• base
• nonn
• more

Comments

Numbers k such that A066417(k) divides A130846(k).

Similar to A308486 where divisors are considered.

Examples

			Anti-divisors of 1656 are 7, 11, 16, 43, 48, 77, 144, 301, 368, 473, 1104 and their sum is 2592. Then, 711164348771443013684731104 / 2592 = 274368961717377705896887.
		

Crossrefs

Cf. A066272, A066417, A130846, A308486.

Programs

Maple

P:=proc(q) local a,b,k,n; for n from 3 to q do a:=0: b:=0:
for k from 2 to n-1 do if abs((n mod k)-k/2)<1 then
a:=a*10^length(k)+k: b:=b+k: fi; od; if frac(a/b)=0 then print(n);
fi; od; end: P(10^6);

Python

from itertools import islice, count
from sympy.ntheory.factor_ import antidivisors
def A308533gen(): # generator of terms
    for n in count(3):
        a = antidivisors(n)
        if int(''.join(str(s) for s in a)) % sum(a) == 0:
            yield n
A308533_list = list(islice(A308533gen(),22)) # Chai Wah Wu, Dec 08 2021

Extensions

a(22)-a(30) from Chai Wah Wu, Dec 08 2021

a(31)-a(32) from Chai Wah Wu, Dec 14 2021