A249431 a(n) = A249151(n) - n.

1, 0, 0, -2, 0, -3, 0, -6, -6, -5, 0, -4, 0, -7, -10, -14, 0, -15, 0, -15, -14, -11, 0, -12, -20, -13, -24, -21, 0, -4, 0, -30, -22, -17, -28, 1, 0, -19, -26, 1, 0, -35, 0, -33, -21, -23, 0, -28, -42, -45, -34, -39, 0, -51, -44, -20, -38, -29, 0, -12, 0, -31, 1, -62, -52, -55, 0, -51, -46, -20, 0, -30, 0

Offset: 0

Author

Antti Karttunen, Nov 02 2014

Keywords

• sign
• changed

Comments

It seems that A006093 gives the positions of zeros.

Links

• Chai Wah Wu, Table of n, a(n) for n = 0..10000 (terms 0..4096 from Antti Karttunen)

Crossrefs

A249433 and A249434 give the positions of negative and nonnegative values, respectively.

A249430 gives the position where +n appears for the first time, A249432 the positions of records of positive values.

Cf. A006093, A249151.

Programs

Python

from itertools import count
from collections import Counter
from math import comb
from sympy import factorint
def A249431(n):
    p = sum((Counter(factorint(comb(n,i))) for i in range(n+1)),start=Counter())
    for m in count(1):
        f = Counter(factorint(m))
        if not f<=p:
            return m-1-n
        p -= f # Chai Wah Wu, Aug 19 2025

Scheme

(definec (A249431 n) (- (A249151 n) n))

Formula

a(n) = A249151(n) - n.