cp's OEIS Frontend

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

%I A023196 #76 Sep 07 2023 11:09:50
%S A023196 6,12,18,20,24,28,30,36,40,42,48,54,56,60,66,70,72,78,80,84,88,90,96,
%T A023196 100,102,104,108,112,114,120,126,132,138,140,144,150,156,160,162,168,
%U A023196 174,176,180,186,192,196,198,200,204,208,210,216,220,222,224,228,234,240,246,252
%N A023196 Nondeficient numbers: numbers k such that sigma(k) >= 2k; union of A000396 and A005101.
%C A023196 Also called the non-deficient numbers.
%C A023196 If k is a term, so is every positive multiple of k. The "primitive" terms form A006039.
%C A023196 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 A023196 Also, union of pseudoperfect and weird numbers. Cf. A005835, A006037. - _Franklin T. Adams-Watters_, Mar 29 2006
%C A023196 k is in the sequence if and only if A004125(k-1) > A004125(k). - _Jaycob Coleman_, Mar 31 2014
%C A023196 Like the abundant numbers, this sequence has density between 0.2474 and 0.2480, see A005101. - _Charles R Greathouse IV_, Nov 30 2022
%H A023196 T. D. Noe, <a href="/A023196/b023196.txt">Table of n, a(n) for n = 1..1000</a>
%H A023196 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 A023196:=n->`if`(numtheory[sigma](n)>=2*n, n, NULL): seq(A023196(n), n=1..380); # _Wesley Ivan Hurt_, Apr 18 2017
%t A023196 Select[Range[300], DivisorSigma[1, #] >= 2# &] (* _Harvey P. Dale_, Sep 26 2014 *)
%o A023196 (PARI) is(n)=sigma(n,-1)>=2 \\ _Charles R Greathouse IV_, Mar 09 2014
%o A023196 (GAP) Filtered([1..260],n->Sigma(n)>=2*n); # _Muniru A Asiru_, Dec 04 2018
%o A023196 (Magma) [n: n in [1..300] | not (2*n gt DivisorSigma(1,n))]; // _Vincenzo Librandi_, Dec 05 2018
%Y A023196 Cf. A000203, A004125, A006039, A000396, A005101.
%K A023196 nonn,nice
%O A023196 1,1
%A A023196 _David W. Wilson_