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.

4, 8, 8, 1909, 558031, 783975, 185363811, 1584002413

Offset

1,1

Links

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

Example

sigma(1909) - 1909 = 107 that is a prime number;
sigma(1910) - 1910 = 1546 = 2*773;
sigma(1911) - 1911 = 1281 = 3*7*61;
sigma(1912) - 1912 = 1688 = 2*2*2*211.
No other number < 1909 has this property and therefore a(4) = 1909.

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)-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. A001065, A086560, A072875, A279520.

Sequence in context: A095806 A096872 A123959 * A340721 A096412 A153109

Adjacent sequences: A279515 A279516 A279517 * A279519 A279520 A279521

Keyword

nonn,more

Author

Paolo P. Lava, Dec 14 2016

Extensions

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

Status

approved