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

1,1

Links

Table of n, a(n) for n=1..8.

Example

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.

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);

Crossrefs

Cf. A003415, A086560, A072875, A279518.

Sequence in context: A112822 A033589 A077289 * A309378 A221933 A110342

Adjacent sequences: A279517 A279518 A279519 * A279521 A279522 A279523

Keyword

nonn,more

Author

Paolo P. Lava, Dec 14 2016

Extensions

a(7)-a(8) from Giovanni Resta, Dec 14 2016

Status

approved