A175591 a(n) = (sigma(n-th Zumkeller number)/2) - (n-th Zumkeller number).

0, 2, 1, 6, 0, 6, 5, 6, 14, 6, 4, 24, 6, 2, 6, 13, 28, 2, 27, 30, 6, 1, 32, 12, 6, 60, 30, 36, 6, 28, 36, 40, 29, 72, 6, 10, 93, 6, 62, 36, 48, 9, 78, 84, 32, 6, 28, 52, 39, 132, 6, 112, 6, 34, 96, 90, 7, 60, 80, 6, 48, 134, 6, 45, 28, 108, 6, 61, 102, 160, 38, 48, 72, 22, 26, 6, 225, 28, 6

Offset

1,2

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Formula

a(n) = A175582(n) - A083207(n).

Prog

(Python)
from sympy import divisors
import numpy as np
A175591 = []
for n in range(1, 10**6):
    d = divisors(n)
    s = sum(d)
    if not s % 2 and 2*n <= s:
        d.remove(n)
        s2, ld = int(s/2-n), len(d)
        z = np.zeros((ld+1, s2+1), dtype=int)
        for i in range(1, ld+1):
            y = min(d[i-1], s2+1)
            z[i, range(y)] = z[i-1, range(y)]
            z[i, range(y, s2+1)] = np.maximum(z[i-1, range(y, s2+1)], z[i-1, range(0, s2+1-y)]+y)
            if z[i, s2] == s2:
                A175591.append(s2)
                break
# Chai Wah Wu, Aug 20 2014

Crossrefs

Cf. A083207, A175582.

Sequence in context: A335931 A091615 A213279 * A187784 A370901 A198812

Adjacent sequences: A175588 A175589 A175590 * A175592 A175593 A175594

Keyword

nonn

Author

Vladislav-Stepan Malakhovsky and Juri-Stepan Gerasimov, Jul 19 2010

Extensions

Inserted a(45) and corrected a(73) by Chai Wah Wu, Aug 20 2014

Name edited by Ivan N. Ianakiev, Jan 18 2020

Status

approved