A243104 Odd numbers in A192274.

945, 1575, 2205, 2835, 3465, 4095, 4725, 6435, 6615, 6825, 7245, 7425, 7875, 8085, 8505, 8925, 9135, 9555, 9765, 10395, 11655, 12285, 12915, 13545, 14805, 15015, 16065, 16695, 17955, 18585, 19215, 19635, 19845, 20475, 21105, 21735, 22275, 22365, 22995, 23205

Offset

1,1

Links

Chai Wah Wu, Table of n, a(n) for n = 1..500

Prog

(Python)
from sympy import divisors
import numpy as np
A243104 = []
for n in range(3, 10**4, 2):
    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:
                d2 = [2*x for x in d if n > 2*x and n % (2*x)] + \
                [x for x in divisors(2*n-1) if n > x >=2 and n % x] + \
                [x for x in divisors(2*n+1) if n > x >=2 and n % x]
                s, dmax = sum(d2), max(d2)
                if not s % 2 and 2*dmax <= s:
                    d2.remove(dmax)
                    s2, ld = int(s/2-dmax), len(d2)
                    z = np.zeros((ld+1, s2+1), dtype=int)
                    for i in range(1, ld+1):
                        y = min(d2[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:
                            A243104.append(n)
                            break
                break

Crossrefs

Cf. A192274.

Sequence in context: A005231 A174865 A174535 * A381547 A006038 A287646

Adjacent sequences: A243101 A243102 A243103 * A243105 A243106 A243107

Keyword

nonn

Author

Chai Wah Wu, Aug 19 2014

Status

approved