cp's OEIS Frontend

A045983 Numbers k such that n or more consecutive integers starting at k have the same number of distinct prime divisors.

%I A045983 #18 Jun 23 2025 00:41:10
%S A045983 1,2,2,2,54,91,141,141,44360,48919,218972,526095,526095,526095,
%T A045983 17233173,127890362,29138958036,118968284928,118968284928,
%U A045983 585927201062,585927201062,585927201062,585927201062,313978488186061,453918847597184,453918847597184,455626105596320
%N A045983 Numbers k such that n or more consecutive integers starting at k have the same number of distinct prime divisors.
%C A045983 a(n) = smallest number k such that the n numbers from k through n+k-1 have the same number of prime divisors.
%C A045983 a(24) > 10^12. - _Donovan Johnson_, Mar 29 2013
%C A045983 a(28) > 2 * 10^15. - _Toshitaka Suzuki_, Jun 22 2025
%e A045983 a(5) = 54 as 54, 55, 56, 57, 58 all have 2 prime divisors.
%o A045983 (PARI) v=vector(16); n=0; c1=0; for(k=1, 127890377, c2=omega(k); if(c1==c2, n++; if(v[n]==0, v[n]=k-n+1; print(n " " v[n])), n=1; c1=c2)) /* _Donovan Johnson_, Mar 29 2013 */
%Y A045983 Cf. A006049, A075028, A075031.
%K A045983 nonn
%O A045983 1,2
%A A045983 _David W. Wilson_
%E A045983 a(18)-a(23) from _Donovan Johnson_, Mar 29 2013
%E A045983 a(24)-a(27) from _Toshitaka Suzuki_, Jun 22 2025