cp's OEIS Frontend

A340159 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.

%I A340159 #20 Mar 19 2024 03:17:00
%S A340159 1,1,61,421,211082,11238341,16788951482,41126483642
%N A340159 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 A340159 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 A340159 Corresponding values of tau(a(n)): 1, 1, 2, 2, 4, 4, 4, ...
%C A340159 a(8) <= 41126483642. - _David A. Corneth_, Dec 31 2020
%C A340159 Any subsequent terms are > 10^11. - _Lucas A. Brown_, Mar 18 2024
%H A340159 Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/A340159.py">Python program</a>.
%e A340159 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 A340159 (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 A340159 a(n) = my(m=1); while(!isok(m, n), m++); m; \\ _Michel Marcus_, Dec 30 2020
%o A340159 (Python) # see LINKS
%Y A340159 Cf. A294528 for similar sequence with primes.
%Y A340159 Cf. A000005, A063446, A339778, A340157, A340158.
%K A340159 nonn,more,hard
%O A340159 1,3
%A A340159 _Jaroslav Krizek_, Dec 29 2020
%E A340159 a(7) from _Jinyuan Wang_, Dec 31 2020
%E A340159 a(8) from _Lucas A. Brown_, Mar 18 2024