A390483 Values of L(2^n), where L(n) is the summatory function of the Liouville function A008836(n).

1, 0, 0, -2, 0, -6, -2, -10, -6, -20, -20, -22, -64, -22, -144, -74, -188, -212, -326, -642, -332, -1680, -582, -2904, -1696, -5798, -4478, -8942, -13240, -9018, -34472, -16158, -54228, -56482, -99052, -130104, -121048, -331382, -177706, -777622, -422988

Offset

0,4

Links

Henri Lifchitz, Table of n, a(n) for n = 0..67

Eric Weisstein's World of Mathematics, Liouville Function.

Formula

a(n) = A002819(2^n).

Mathematica

Table[Sum[LiouvilleLambda[k], {k, 1, 2^n}], {n, 0, 15}]

Prog

(PARI) a(n) = sum(i=1, 2^n, (-1)^bigomega(i));
(Python)
from math import isqrt
from functools import lru_cache
@lru_cache(maxsize=None)
def A002321(n):
    if n == 0:
        return 0
    c, j = n, 2
    k1 = n//j
    while k1 > 1:
        j2 = n//k1 + 1
        c += (j2-j)*A002321(k1)
        j, k1 = j2, n//j2
    return j-c
def A390483(n):
    m = 1<<n
    c, j, k1 = isqrt(m)+1, 1, m
    while k1 > 1:
        j2 = isqrt(m//k1) + 1
        c += (j2-j)*A002321(k1)
        j, k1 = j2, m//j2**2
    return c-j # Chai Wah Wu, Nov 13 2025

Crossrefs

Cf. A002321, A002819, A008836, A090410.

Sequence in context: A021833 A196072 A261883 * A294779 A049257 A054877

Adjacent sequences: A390480 A390481 A390482 * A390484 A390485 A390486

Keyword

sign

Author

Henri Lifchitz, Nov 07 2025

Status

approved