cp's OEIS Frontend

A279518 Start of first run of n successive numbers in which the sum of aliquot parts of the i-th number has exactly i prime factors, for i = 1..n.

%I A279518 #7 Dec 15 2016 11:38:41
%S A279518 4,8,8,1909,558031,783975,185363811,1584002413
%N A279518 Start of first run of n successive numbers in which the sum of aliquot parts of the i-th number has exactly i prime factors, for i = 1..n.
%e A279518 sigma(1909) - 1909 = 107 that is a prime number;
%e A279518 sigma(1910) - 1910 = 1546 = 2*773;
%e A279518 sigma(1911) - 1911 = 1281 = 3*7*61;
%e A279518 sigma(1912) - 1912 = 1688 = 2*2*2*211.
%e A279518 No other number < 1909 has this property and therefore a(4) = 1909.
%p A279518 with(numtheory): P:=proc(q) local a,b,d,i,j,k,ok,n; d:=1;
%p A279518 for k from 1 to q do for n from d to q do ok:=1; for j from 1 to k do
%p A279518 b:=ifactors(sigma(n+j-1)-n-j+1)[2]; if add(b[i][2],i=1..nops(b))<>j then ok:=0; break; fi; od;
%p A279518 if ok=1 then d:=n; print(n); break; fi; od; od; end: P(10^12);
%Y A279518 Cf. A001065, A086560, A072875, A279520.
%K A279518 nonn,more
%O A279518 1,1
%A A279518 _Paolo P. Lava_, Dec 14 2016
%E A279518 a(7)-a(8) from _Giovanni Resta_, Dec 14 2016