%I #20 Mar 19 2024 03:17:00
%S 1,1,61,421,211082,11238341,16788951482,41126483642
%N 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.
%C 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).
%C Corresponding values of tau(a(n)): 1, 1, 2, 2, 4, 4, 4, ...
%C a(8) <= 41126483642. - _David A. Corneth_, Dec 31 2020
%C Any subsequent terms are > 10^11. - _Lucas A. Brown_, Mar 18 2024
%H Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/A340159.py">Python program</a>.
%e a(3) = 61 because 61, 62 and 63 have 2, 4, and 6 divisors respectively and there is no smaller number having this property.
%o (PARI) isok(m, n) = {my(k=numdiv(m)); for (i=1, n-1, if (numdiv(m+i) != (i+1)*k, return (0));); return(1);}
%o a(n) = my(m=1); while(!isok(m, n), m++); m; \\ _Michel Marcus_, Dec 30 2020
%o (Python) # see LINKS
%Y Cf. A294528 for similar sequence with primes.
%Y Cf. A000005, A063446, A339778, A340157, A340158.
%K nonn,more,hard
%O 1,3
%A _Jaroslav Krizek_, Dec 29 2020
%E a(7) from _Jinyuan Wang_, Dec 31 2020
%E a(8) from _Lucas A. Brown_, Mar 18 2024