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A374816
a(n) is the least k > a(n-1) such that k - a(i) for i = 0 .. n-1 all have exactly n prime factors, counted with multiplicity; a(0) = 0.
0
0, 2, 6, 116, 350, 14130, 6626906, 998632866, 150811201250
OFFSET
0,2
COMMENTS
A008776(n) and A008776(n) - A008776(n-1) have n prime factors, counted with multiplicity, and it appears that A008776(n) is the least k with this property.
EXAMPLE
a(1) = 2 is prime.
a(2) = 6 = 2 * 3 and 6 - 2 = 4 = 2^2 have 2 prime factors, counted with multiplicity.
a(3) = 116 = 2^2 * 29, 116 - 2 = 114 = 2 * 3 * 19 and 116 - 6 = 110 = 2 * 5 * 11 have 3 prime factors, counted with multiplicity.
MAPLE
A[0]:= 0:
for i from 1 to 6 do
for x from A[i-1]+1 do
if andmap(t -> numtheory:-bigomega(x-t)=i, [seq(A[j], j=0..i-1)]) then
A[i]:= x;
break
fi
od od:
seq(A[i], i=0..6);
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Zak Seidov and Robert Israel, Jul 20 2024
EXTENSIONS
a(8) from Daniel Suteu, Aug 06 2024
STATUS
approved