

A279518


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


1




OFFSET

1,1


LINKS



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+j1)nj+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



KEYWORD

nonn,more


AUTHOR



EXTENSIONS



STATUS

approved



