OFFSET
1,1
COMMENTS
To distinguish this from A259349: "Numbers n with exactly k distinct prime factors" means numbers with A001221(n) = omega(n) = k, which specifies that in the prime factorization n = Product_{i>=1} p_i^(e_i), e_i >= 1, the exponents are ignored, and only the size of the set of the (distinct) p_i is considered. In A259349, the numbers n are products of k distinct primes, which means in the prime factorization of n, all exponents e_i are equal to 1. (If all exponents e_i = 1, the n are squarefree, i.e., in A005117.) Rephrased: the n which are products of k distinct primes have A001221(n) = omega(n) = A001222(n) = bigomega(n) = k, whereas the n which have exactly k distinct prime factors are the superset of (weaker) requirement A001221(n) = omega(n) = k. - R. J. Mathar, Jul 18 2023
LINKS
David A. Corneth, Table of n, a(n) for n = 1..10000
MAPLE
omega := proc(n)
nops(numtheory[factorset](n)) ;
end proc:
for k from 1 do
if omega(k) = 6 then
if omega(k+1) = 6 then
if omega(k+2) = 6 then
print(k) ;
end if;
end if;
end if;
end do:
PROG
(PARI) upto(n) = {my(res = List(), streak = 0); forfactored(i = 2, n, if(#i[2]~ == 6, streak++; if(streak >= 3, listput(res, i[1] - 2)), streak = 0)); res} \\ David A. Corneth, Jul 18 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
R. J. Mathar, Jul 16 2023
EXTENSIONS
More terms from David A. Corneth, Jul 18 2023
STATUS
approved