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A194356
Triangle of divisors of 10^n, each number occurring once.
6
1, 2, 5, 10, 4, 20, 25, 50, 100, 8, 40, 125, 200, 250, 500, 1000, 16, 80, 400, 625, 1250, 2000, 2500, 5000, 10000, 32, 160, 800, 3125, 4000, 6250, 12500, 20000, 25000, 50000, 100000, 64, 320, 1600, 8000, 15625, 31250, 40000, 62500, 125000, 200000, 250000
OFFSET
0,2
COMMENTS
The following rule for divisibility applies: for each term t in the n-th row of the triangle, a positive integer m is divisible by t if the last n digits of m are divisible by t; e.g., for n = 2, since 20 is one of the terms in the 2nd row of the triangle, a number m is divisible by 20 if the last 2 digits of m are divisible by 20. - Martin Renner, Jan 15 2023
LINKS
EXAMPLE
The n-th row of the triangle begins with 2^n and ends with 10^n:
1;
2, 5, 10;
4, 20, 25, 50, 100;
8, 40, 125, 200, 250, 500, 1000;
16, 80, 400, 625, 1250, 2000, 2500, 5000, 10000;
MAPLE
T:={{1}}:
for n from 1 to 9 do
T:={op(T), numtheory[divisors](10^n) minus numtheory[divisors](10^(n-1))};
od:
T; # Martin Renner, Jan 16 2023
MATHEMATICA
Join[{{1}}, Table[Complement[Divisors[10^n], Divisors[10^(n-1)]], {n, 9}]]
PROG
(Python)
from sympy import divisors
A194356 = []
for k in range(0, 7): # shows the terms in the range 10^0 ... 10^6
for divisor in divisors(10**k):
if divisor not in A194356: A194356.append(divisor)
print(A194356) # Karl-Heinz Hofmann, Feb 19 2024
(Python)
from math import isqrt
def A194356(n):
exp = isqrt(n)
aarray = [2**exp, 10**exp]
while aarray[-1] % 2 == 0: aarray.append(aarray[-1]//2)
while aarray[0] * 5 < 10**exp: aarray = [aarray[0]*5] + aarray
return sorted(aarray)[n-exp**2]
print([A194356(n) for n in range(0, 49)]) # Karl-Heinz Hofmann, Feb 19 2024
(PARI) row(n) = my(pow2 = 2^n, pow5 = 5^n); Set(concat(vector(n+1, i, pow5*2^(i-1)), vector(n, i, pow2*5^(i-1)))) \\ David A. Corneth, Feb 19 2024
CROSSREFS
Cf. A000079 (1st column), A011557 (right diagonal).
Cf. A003592 (numbers of the form 2^i*5^j).
Cf. A194357 (divisors of 6^n), A194358 (divisors of 30^n).
Sequence in context: A078322 A252867 A352199 * A227317 A224300 A175467
KEYWORD
nonn,tabf
AUTHOR
T. D. Noe, Aug 25 2011
STATUS
approved