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A341213
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a(n) is the smallest number m such that numbers m, m - 1, m - 2, ..., m - n + 1 have k, 2*k, 3*k, ..., n*k divisors respectively.
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3
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OFFSET
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1,2
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COMMENTS
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a(n) is the smallest number m such that tau(m) = tau(m - 1)/2 = tau(m - 2)/3 = tau(m - 3)/4 = ... = tau(m - n + 1)/n, where tau(k) = the number of divisors of k (A000005).
Corresponding values of numbers k: 1, 2, 2, 2, 4, 4, 4, 4, ...
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LINKS
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EXAMPLE
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a(3) = 47 because 45, 46 and 47 have 6, 4, and 2 divisors respectively and there is no smaller number having this property.
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PROG
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(Python)
d, t = 1, 0
while d*d < n:
if n%d == 0:
t = t+2
d = d+1
if d*d == n:
t = t+1
return t
while n > 0:
nn, t1 = 1, tau(a)
while nn < n and tau(a-nn) == (nn+1)*t1:
nn = nn+1
if nn == n:
print(n, a)
n = n+1
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CROSSREFS
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Cf. A341214 (similar sequence with primes).
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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