A175591 - OEIS

%I #15 Oct 18 2024 18:00:31

%S 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,

%T 28,36,40,29,72,6,10,93,6,62,36,48,9,78,84,32,6,28,52,39,132,6,112,6,

%U 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

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

%H Chai Wah Wu, <a href="/A175591/b175591.txt">Table of n, a(n) for n = 1..10000</a>

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

%o (Python)

%o from sympy import divisors

%o import numpy as np

%o A175591 = []

%o for n in range(1, 10**6):

%o     d = divisors(n)

%o     s = sum(d)

%o     if not s % 2 and 2*n <= s:

%o         d.remove(n)

%o         s2, ld = int(s/2-n), len(d)

%o         z = np.zeros((ld+1, s2+1), dtype=int)

%o         for i in range(1, ld+1):

%o             y = min(d[i-1], s2+1)

%o             z[i, range(y)] = z[i-1, range(y)]

%o             z[i, range(y, s2+1)] = np.maximum(z[i-1, range(y, s2+1)], z[i-1, range(0, s2+1-y)]+y)

%o             if z[i, s2] == s2:

%o                 A175591.append(s2)

%o                 break

%o # _Chai Wah Wu_, Aug 20 2014

%Y Cf. A083207, A175582.

%K nonn

%O 1,2

%A Vladislav-Stepan Malakhovsky and _Juri-Stepan Gerasimov_, Jul 19 2010

%E Inserted a(45) and corrected a(73) by _Chai Wah Wu_, Aug 20 2014

%E Name edited by _Ivan N. Ianakiev_, Jan 18 2020