A194356 Triangle of divisors of 10^n, each number occurring once.
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
Examples
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;
Links
- T. D. Noe, Rows for n = 0..100
Crossrefs
Programs
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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}]] -
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
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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
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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
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