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
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.
Programs
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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);
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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
Comments