A308486 -id:A308486

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A308533

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

+10
1

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

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

Similar to A308486 where divisors are considered.

LINKS

Table of n, a(n) for n=1..32.

EXAMPLE

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.

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);

PROG

(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

CROSSREFS

Cf. A066272, A066417, A130846, A308486.

KEYWORD

base,nonn,more

AUTHOR

Paolo P. Lava, Jun 06 2019

EXTENSIONS

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

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

STATUS

approved

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