A393185 Numbers that are the smaller of two distinct positive integers with opposite abundances, where this pair of abundances occurs for the first time; sorted by the larger term.

5, 3, 13, 6, 25, 11, 29, 22, 58, 87, 61, 84, 112, 73, 108, 59, 156, 46, 50, 97, 19, 157, 214, 79, 192, 142, 193, 181, 27, 269, 141, 243, 312, 280, 158, 94, 53, 229, 109, 106, 180, 358, 252, 89, 384, 47, 406, 120, 277, 446, 127, 433, 17, 337, 261, 250, 101, 421

Offset

1,1

Comments

The larger positive integer is A393184(n), the deficiency of a(n) is A393186(n).

For each n, the pair (A393185(n), A393184(n)) contains one abundant number and one deficient number. Exception: at n = 4, the pair (6, 28) consists of two perfect numbers.

Links

Felix Huber, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Abundance

Example

a(1) = 5 since (5, A393184(1)) = (5, 12) is the first pair with opposite abundances +-4.
a(4) = 6 since (6, A393184(4)) = (6, 28) is the first pair with abundances 0 and 0.
a(12) = 112 since (112, A393184(12)) = (112, 118) is the first pair with opposite abundances +-56.

Maple

A393185List := proc(N)
    option remember;
    local a, t, s, k, d, i;
    a := `if`(N < 28, [], [[28, 6]]);
    t := table();
    s := table();
    for k to N do
        d := NumberTheory:-sigma(k) - 2*k;
        if not assigned(t[d]) then
            t[d] := k;
            if assigned(t[-d]) then
                if not assigned(s[k]) then
                    a := [op(a), [k, min(k, t[-d])]];
                    s[k] := 1;
                end if;
            end if;
        end if;
    end do;
    a := sort(a);
    seq(a[i][2], i = 2 .. nops(a));
end proc:
A393185List(588);

Crossrefs

Cf. A000203, A000396, A002025, A005100, A005101, A033879, A033880, A330901, A331181, A335253, A335254, A393184, A393186.

Sequence in context: A104587 A300940 A131939 * A205522 A111744 A083781

Adjacent sequences: A393182 A393183 A393184 * A393186 A393187 A393188

Keyword

nonn,easy

Author

Felix Huber, Feb 08 2026

Status

approved