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.
1, 7, 47, 1019, 154379, 59423129, 3100501318, 126544656838
Offset: 1
Examples
a(3) = 47 because 45, 46 and 47 have 6, 4, and 2 divisors respectively and there is no smaller number having this property.
Programs
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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
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
Comments