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.
6, 105, 1001, 2945, 240485, 1671414, 22551962, 22551962
Offset: 1
Examples
2945' = 839 that is a prime number; 2946' = 2461 = 23*107; 2947' = 428 = 2*2*107; 2948' = 3260 = 2*2*5*163. No other number < 2945 has this property and therefore a(4) = 2945.
Programs
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Maple
with(numtheory): P:=proc(q) local a,b,d,i,j,k,ok,n; d:=1; for k from 1 to q do for n from d to q do ok:=1; for j from 1 to k do b:=ifactors(sigma(n+j-1))[2]; if add(b[i][2],i=1..nops(b))<>j then ok:=0; break; fi; od; if ok=1 then d:=n; print(n); break; fi; od; od; end: P(10^12);
Extensions
a(7)-a(8) from Giovanni Resta, Dec 14 2016