The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A171642 Non-deficient numbers with odd sigma such that the sum of the even divisors is twice the sum of the odd divisors. 1
 18, 162, 450, 882, 1458, 2178, 2450, 3042, 4050, 5202, 6050, 6498, 7938, 8450, 9522, 11250, 13122, 15138, 17298, 19602, 22050, 24642, 27378, 30258, 33282, 36450, 39762, 43218, 46818, 50562, 54450, 58482, 61250, 62658, 66978, 71442, 76050, 80802, 85698 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Numbers which are non-deficient (2n <= sigma(n)) [A023196] such that sigma(n) [A000203] is odd and the sum of the even divisors [A074400] is twice the sum of the odd divisors [A000593]. The sequence of terms which are not of the form 72*k^2 + 72*k + 18 starts: 2450, 6050, 8450, 61250, 120050, 151250, 211250, 296450. LINKS Donovan Johnson, Table of n, a(n) for n = 1..1000 Peter Luschny, Zumkeller Numbers. EXAMPLE Example: divisors(18) = {1, 2, 3, 6, 9, 18}, sigma(18) = 39, and 2 + 6 + 18 = 2*(1 + 3 + 9). MAPLE with(numtheory): A171642 := proc(n) local k, s, a; s := sigma(n); a := add(k, k=select(x->type(x, odd), divisors(n))); if 3*a = s and 2*n <= s and type(s, odd) then n else NULL fi end: PROG (Python) from sympy import divisors A171642 = [] for n in range(1, 10**5): ....d = divisors(n) ....s = sum(d) ....if s % 2 and 2*n <= s and s == 3*sum([x for x in d if x % 2]): ........A171642.append(n) # Chai Wah Wu, Aug 20 2014 CROSSREFS Cf. A000203, A023196, A074400, A000593. Cf. A171641, A083207, A023196, A077591, A137933. Sequence in context: A119004 A002698 A222914 * A158808 A271899 A128797 Adjacent sequences: A171639 A171640 A171641 * A171643 A171644 A171645 KEYWORD nonn AUTHOR Peter Luschny, Dec 14 2009 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 22 14:42 EDT 2024. Contains 372755 sequences. (Running on oeis4.)