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A171641 Non-deficient numbers with even sigma which are not Zumkeller. 3
738, 748, 774, 846, 954, 1062, 1098, 1206, 1278, 1314, 1422, 1494, 1602, 1746, 1818, 1854, 1926, 1962, 2034, 2286, 2358, 2466, 2502, 2682, 2718, 2826, 2934, 3006, 3114, 3222, 3258, 3438, 3474, 3492, 3546, 3582, 3636, 3708, 3798, 3852, 3924 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers which are non-deficient (sigma(n) >= 2n) [A023196] such that sigma(n) [A000203] is even but which are not Zumkeller numbers [A083207], i.e., the positive factors of n cannot be partitioned into two disjoint parts so that the sums of the two parts are equal.

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..1000

Peter Luschny, Zumkeller Numbers.

MATHEMATICA

Reap[For[n = 2, n <= 4000, n = n+2, sigma = DivisorSigma[1, n]; If[sigma >= 2n && EvenQ[sigma] && Coefficient[ Times @@ (1 + x^Divisors[n]) // Expand, x, sigma/2] == 0, Print[n]; Sow[n]]]][[2, 1]] (* Jean-Fran├žois Alcover, Jul 26 2013 *)

PROG

(Python)

from sympy import divisors

import numpy as np

A171641 = []

for n in range(2, 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[ld, s2] != s2:

............A171641.append(n)

# Chai Wah Wu, Aug 19 2014

CROSSREFS

Cf. A083207, A023196

Sequence in context: A004078 A218596 A043633 * A251814 A251647 A204289

Adjacent sequences:  A171638 A171639 A171640 * A171642 A171643 A171644

KEYWORD

nonn

AUTHOR

Peter Luschny, Dec 14 2009

STATUS

approved

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Last modified September 22 00:25 EDT 2017. Contains 292326 sequences.