Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #76 Sep 07 2023 11:09:50
%S 6,12,18,20,24,28,30,36,40,42,48,54,56,60,66,70,72,78,80,84,88,90,96,
%T 100,102,104,108,112,114,120,126,132,138,140,144,150,156,160,162,168,
%U 174,176,180,186,192,196,198,200,204,208,210,216,220,222,224,228,234,240,246,252
%N Nondeficient numbers: numbers k such that sigma(k) >= 2k; union of A000396 and A005101.
%C Also called the non-deficient numbers.
%C If k is a term, so is every positive multiple of k. The "primitive" terms form A006039.
%C 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
%C Also, union of pseudoperfect and weird numbers. Cf. A005835, A006037. - _Franklin T. Adams-Watters_, Mar 29 2006
%C k is in the sequence if and only if A004125(k-1) > A004125(k). - _Jaycob Coleman_, Mar 31 2014
%C Like the abundant numbers, this sequence has density between 0.2474 and 0.2480, see A005101. - _Charles R Greathouse IV_, Nov 30 2022
%H T. D. Noe, <a href="/A023196/b023196.txt">Table of n, a(n) for n = 1..1000</a>
%H Paul Pollack and Carl Pomerance, <a href="https://doi.org/10.1090/BTRAN%2F10">Some problems of Erdős on the sum-of-divisors function</a>, For Richard Guy on his 99th birthday: May his sequence be unbounded, Trans. Amer. Math. Soc. Ser. B (2016) Vol. 3, 1-26.
%p A023196:=n->`if`(numtheory[sigma](n)>=2*n, n, NULL): seq(A023196(n), n=1..380); # _Wesley Ivan Hurt_, Apr 18 2017
%t Select[Range[300], DivisorSigma[1, #] >= 2# &] (* _Harvey P. Dale_, Sep 26 2014 *)
%o (PARI) is(n)=sigma(n,-1)>=2 \\ _Charles R Greathouse IV_, Mar 09 2014
%o (GAP) Filtered([1..260],n->Sigma(n)>=2*n); # _Muniru A Asiru_, Dec 04 2018
%o (Magma) [n: n in [1..300] | not (2*n gt DivisorSigma(1,n))]; // _Vincenzo Librandi_, Dec 05 2018
%Y Cf. A000203, A004125, A006039, A000396, A005101.
%K nonn,nice
%O 1,1
%A _David W. Wilson_