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

Author

Paolo P. Lava, Dec 14 2016

Keywords

• nonn
• more

Examples

			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.
		

Crossrefs

Cf. A001065, A086560, A072875, A279520.

Programs

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);

Extensions

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