A263837 Non-abundant numbers (or nonabundant numbers): complement of A005101; numbers k for which sigma(k) <= 2*k.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 37, 38, 39, 41, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 55, 57, 58, 59, 61, 62, 63, 64, 65, 67, 68, 69, 71, 73, 74, 75, 76, 77, 79, 81, 82, 83, 85, 86, 87, 89, 91, 92, 93, 94, 95, 97, 98, 99

Offset: 1

Author

N. J. A. Sloane, Oct 30 2015

Keywords

• nonn

Comments

For all n, A003961(a(n)) is in A005100. - Antti Karttunen, Aug 28 2020

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• 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 3 (2016), 1-26.

Crossrefs

Union of A000396 and A005100.

Cf. A005101 (complement), A023196, A294935 (characteristic function).

Cf. A000203, A001065, A003961.

Programs

Haskell

a263837 n = a263837_list !! (n-1)
a263837_list = filter (\x -> a001065 x <= x) [1..]
-- Reinhard Zumkeller, Oct 31 2015

Maple

isA263837 := proc(n)
    if 2*n-numtheory[sigma](n) >=0 then
        true;
    else
        false;
    end if;
end proc:
A263837 := proc(n)
    option remember;
    local a;
    if n =1 then
        1;
    else
        for a from procname(n-1)+1 do
            if isA263837(a) then
                return a;
            end if;
        end do:
    end if;
end proc:
seq(A263837(n),n=1..100) ; # R. J. Mathar, Jun 06 2024

Mathematica

Select[Range[100], DivisorSigma[1, #] <= 2*# &] (* Amiram Eldar, Mar 14 2024 *)

PARI

isok(n) = sigma(n) <= 2*n; \\ Michel Marcus, Dec 27 2015

Formula

A001065(a(n)) <= a(n). - Reinhard Zumkeller, Oct 31 2015

Extensions

Additional description to the definition added by Antti Karttunen, Aug 28 2020