A023196 Nondeficient numbers: numbers k such that sigma(k) >= 2k; union of A000396 and A005101.

6, 12, 18, 20, 24, 28, 30, 36, 40, 42, 48, 54, 56, 60, 66, 70, 72, 78, 80, 84, 88, 90, 96, 100, 102, 104, 108, 112, 114, 120, 126, 132, 138, 140, 144, 150, 156, 160, 162, 168, 174, 176, 180, 186, 192, 196, 198, 200, 204, 208, 210, 216, 220, 222, 224, 228, 234, 240, 246, 252

Offset: 1

Author

David W. Wilson

Keywords

• nonn
• nice

Comments

Also called the non-deficient numbers.

If k is a term, so is every positive multiple of k. The "primitive" terms form A006039.

The sequence of numbers k that give local minima for A004125, i.e., such that A004125(k-1) > A004125(k) and A004125(k) < A004125(k+1) coincides with this sequence for the first 1014 terms. Then there appears 4095 which is a term of A023196 but is not a local minimum. - Max Alekseyev, Jan 26 2005

Also, union of pseudoperfect and weird numbers. Cf. A005835, A006037. - Franklin T. Adams-Watters, Mar 29 2006

k is in the sequence if and only if A004125(k-1) > A004125(k). - Jaycob Coleman, Mar 31 2014

Like the abundant numbers, this sequence has density between 0.2474 and 0.2480, see A005101. - Charles R Greathouse IV, Nov 30 2022

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000
• Paul Pollack and Carl Pomerance, Some problems of Erdős on the sum-of-divisors function, For Richard Guy on his 99th birthday: May his sequence be unbounded, Trans. Amer. Math. Soc. Ser. B (2016) Vol. 3, 1-26.

Crossrefs

Cf. A000203, A004125, A006039, A000396, A005101.

Programs

GAP

Filtered([1..260],n->Sigma(n)>=2*n); # Muniru A Asiru, Dec 04 2018

Magma

[n: n in [1..300] | not (2*n gt DivisorSigma(1,n))]; // Vincenzo Librandi, Dec 05 2018

Maple

A023196:=n->`if`(numtheory[sigma](n)>=2*n, n, NULL): seq(A023196(n), n=1..380); # Wesley Ivan Hurt, Apr 18 2017

Mathematica

Select[Range[300], DivisorSigma[1, #] >= 2# &] (* Harvey P. Dale, Sep 26 2014 *)

PARI

is(n)=sigma(n,-1)>=2 \\ Charles R Greathouse IV, Mar 09 2014