A393206 a(n) is the number of partitions of A005101(n) into distinct abundant numbers.

1, 1, 1, 1, 2, 2, 1, 3, 3, 5, 3, 6, 7, 3, 9, 11, 7, 13, 6, 18, 20, 11, 25, 17, 31, 17, 36, 46, 54, 65, 77, 61, 94, 111, 132, 93, 157, 185, 219, 179, 261, 304, 357, 278, 421, 359, 489, 392, 577, 671, 552, 780, 679, 909, 1056, 1226, 1418, 1642, 1895, 1709, 2186, 2526

Offset

1,5

Links

Felix Huber, Table of n, a(n) for n = 1..5084

Eric Weisstein's World of Mathematics, Abundant Number

Eric Weisstein's World of Mathematics, Partition

Example

The a(10) = 5 partitions of A005101(10) = 54 are [54], [12, 42], [18, 36], [24, 30] and [12, 18, 24].

Maple

with(NumberTheory):
d := proc(i) option remember; sigma(i) > 2*i; end proc:
c := proc(i) option remember; `if`(i = 0, 0, c(i - 1) + `if`(d(i), i, 0)); end proc:
b := proc(n, i) option remember; `if`(n = 0, 1, `if`(i = 0 or c(i) < n, 0, b(n, i - 1) + `if`(i <= n and d(i), b(n - i, i - 1), 0))); end proc:
a := proc(n) option remember; local s, m, k, i;
    s := proc(i, j, n) option remember; `if`(j >= n, i, s(i + 1, `if`(d(i + 1), j + 1, j), n)) end proc;
    m := `if`(n = 1, 12, a(n - 1)[1]);
    k := `if`(n = 1, 1, n - 1);
    i := s(m, k, n);
    [i, b(i, i)];
end proc:
A393206 := n -> a(n)[2]:
seq(A393206(n), n = 1 .. 62);

Crossrefs

Cf. A000009, A000203, A005101, A097798, A393252.

Sequence in context: A117894 A177762 A109380 * A167754 A374434 A372688

Adjacent sequences: A393203 A393204 A393205 * A393207 A393208 A393209

Keyword

nonn

Author

Felix Huber, Feb 13 2026

Status

approved