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A341213
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.
3
1, 7, 47, 1019, 154379, 59423129, 3100501318, 126544656838
OFFSET
1,2
COMMENTS
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, ...
EXAMPLE
a(3) = 47 because 45, 46 and 47 have 6, 4, and 2 divisors respectively and there is no smaller number having this property.
PROG
(Python)
def tau(n): # A000005
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
n, a = 1, 1 # corrected by Martin Ehrenstein, Apr 14 2021
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
a = a+1 # A.H.M. Smeets, Feb 07 2021
CROSSREFS
Cf. A341214 (similar sequence with primes).
Sequence in context: A368295 A268063 A015097 * A201176 A013400 A013399
KEYWORD
nonn,more
AUTHOR
Jaroslav Krizek, Feb 07 2021
EXTENSIONS
a(6) from Amiram Eldar, Feb 07 2021
a(7) from Jinyuan Wang, Feb 08 2021
a(1) corrected and extended with a(8) by Martin Ehrenstein, Apr 14 2021
STATUS
approved