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, 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.

Links

Table of n, a(n) for n=0..8.

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

Cf. A001222, A008776, A361228.

Sequence in context: A156500 A264889 A365669 * A231537 A303441 A377064

Adjacent sequences: A374813 A374814 A374815 * A374817 A374818 A374819

Keyword

nonn,more

Author

Zak Seidov and Robert Israel, Jul 20 2024

Extensions

a(8) from Daniel Suteu, Aug 06 2024

Status

approved