A395824 Record lengths of runs of consecutive integers k such that Omega(k) is even.

1, 2, 3, 4, 5, 7, 9, 12, 13, 15, 17, 18, 19, 20, 24, 28, 33, 34, 35, 37, 38, 41, 44

Offset

1,2

Comments

Equivalently, record lengths of runs where the Liouville function A008836(k) is 1.

For m >= 1, let r(m) be the largest k >= 0 such that A001222(m), ..., A001222(m+k-1) are even. This sequence lists the successive record values of r(m).

Links

Table of n, a(n) for n=1..23.

Example

The first record runs have lengths 1, 2, 3, 4, 5 and occur at 1..1, 9..10, 14..16, 33..36, 54..58.

Prog

(Python)
from sympy import factorint
A001222 = []
for i in range(1, 10**7 + 1):
    A001222.append(sum(factorint(i).values()))
seq_record_length_even = []
even_record = 0
counter = 0
for i in A001222:
    if i%2==0:
        counter += 1
    else:
        if counter > even_record:
            even_record = counter
            seq_record_length_even.append(counter)
        counter = 0
print(seq_record_length_even)

Crossrefs

Cf. A001222, A395823, A066829, A028260, A066793.

Sequence in context: A039850 A238486 A238482 * A383065 A368483 A033100

Adjacent sequences: A395819 A395820 A395823 * A395825 A395826 A395827

Keyword

nonn,more

Author

Anselm Hudde, May 07 2026

Status

approved