A391317 a(n) is the smallest positive integer that has at least one subset of proper divisors that adds to the n-th weird number (A006037(n)).

48, 420, 1680, 2520, 3120, 3360, 3780, 4200, 4200, 4320, 4620, 4620, 4680, 5040, 5040, 5040, 5040, 5040, 5040, 5040, 6120, 6300, 6300, 6300, 6720, 6720, 6720, 6720, 6720, 7200, 7560, 7560, 7560, 7560, 7560, 7560, 7560, 8400, 8400, 8400, 8400, 9240, 9240, 9240, 9240

Offset

1,1

Comments

This sequence is conjectured to be a subsequence of A005101.

Links

Table of n, a(n) for n=1..45.

Example

a(1) = 48 because 48 is the smallest positive integer that has at least one subset of proper divisors that adds to A006037(1) = 70: {1, 2, 3, 4, 8, 12, 16, 24}, {1, 3, 6, 8, 12, 16, 24} and {4, 6, 8, 12, 16, 24} add to 70.

Maple

with(numtheory):
c := proc(n, k) local b, l; l:= sort([(divisors(n) minus {n})[]]):
    b := proc(m, i) option remember; `if`(m=0, 1, `if`(i<1, 0, b(m, i-1)+`if`(l[i]>m, 0, b(m-l[i], i-1))))
    end; forget(b):
    b(k, nops(l))
end:
A391317List := proc(); # To calculate the first 45 terms
    local a, i, k, l;
    a:=[];
    l := [70, 836, 4030, 5830, 7192, 7912, 9272, 10430, 10570, 10792, 10990, 11410, 11690, 12110, 12530, 12670, 13370, 13510, 13790, 13930, 14770, 15610, 15890, 16030, 16310, 16730, 16870, 17272, 17570, 17990, 18410, 18830, 18970, 19390, 19670, 19810, 20510, 21490, 21770, 21910, 22190, 23170, 23590, 24290, 24430];
    for i in l do
        for k from 2*floor((sqrt(1 + 8*i) - 1)/2) do
            if sigma(k) - k >= i and c(k, i) > 0 then
                a := [op(a), k];
                break
            fi
        od
    od;
    return op(a)
end proc;
A391317List();

Crossrefs

Cf. A005101, A005835, A006037.

Sequence in context: A019558 A339761 A232917 * A172201 A249293 A347168

Adjacent sequences: A391314 A391315 A391316 * A391318 A391319 A391320

Keyword

nonn

Author

Felix Huber, Dec 16 2025

Status

approved