cp's OEIS Frontend

A279520 Start of first run of n successive numbers in which the arithmetic derivative of the i-th number has exactly i prime factors, for i = 1..n.

%I A279520 #7 Dec 14 2016 09:15:23
%S A279520 6,105,1001,2945,240485,1671414,22551962,22551962
%N A279520 Start of first run of n successive numbers in which the arithmetic derivative of the i-th number has exactly i prime factors, for i = 1..n.
%e A279520 2945' = 839 that is a prime number;
%e A279520 2946' = 2461 = 23*107;
%e A279520 2947' = 428 = 2*2*107;
%e A279520 2948' = 3260 = 2*2*5*163.
%e A279520 No other number < 2945 has this property and therefore a(4) = 2945.
%p A279520 with(numtheory): P:=proc(q) local a,b,d,i,j,k,ok,n; d:=1;
%p A279520 for k from 1 to q do for n from d to q do ok:=1; for j from 1 to k do
%p A279520 b:=ifactors(sigma(n+j-1))[2]; if add(b[i][2],i=1..nops(b))<>j then ok:=0; break; fi; od;
%p A279520 if ok=1 then d:=n; print(n); break; fi; od; od; end: P(10^12);
%Y A279520 Cf. A003415, A086560, A072875, A279518.
%K A279520 nonn,more
%O A279520 1,1
%A A279520 _Paolo P. Lava_, Dec 14 2016
%E A279520 a(7)-a(8) from _Giovanni Resta_, Dec 14 2016