A308608 For any n > 0 and k >= 0, let w_n(k) be the number of ways to write k as a sum of distinct divisors of n; a(n) = max_{k >= 0} w_n(k).

1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 6, 1, 1, 1, 2, 1, 6, 1, 1, 1, 1, 1, 8, 1, 1, 1, 4, 1, 5, 1, 1, 2, 1, 1, 11, 1, 1, 1, 1, 1, 5, 1, 3, 1, 1, 1, 36, 1, 1, 2, 1, 1, 4, 1, 1, 1, 3, 1, 32, 1, 1, 1, 1, 1, 4, 1, 7, 1, 1, 1, 28, 1, 1

Offset

1,6

Comments

If m and n are coprime then a(m*n) >= a(m)*a(n). - Charlie Neder, Jun 11 2019

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Rémy Sigrist, Colored logarithmic scatterplot of the first 10000 terms (where the color is function of A000005(n))

Example

For n = 6: w_6 takes the following values:
    k     w_6(k)    Corresponding sets of divisors
    --    ------    ------------------------------
     0    1         {}
     1    1         {1}
     2    1         {2}
     3    2         {1, 2}, {3}
     4    1         {1, 3}
     5    1         {2, 3}
     6    2         {1, 2, 3}, {6}
     7    1         {1, 6}
     8    1         {2, 6}
     9    2         {1, 2, 6}, {3, 6}
    10    1         {1, 3, 6}
    11    1         {2, 3, 6}
    12    1         {1, 2, 3, 6}
    >12   0         None
Hence a(6) = 2.

Prog

(PARI) a(n) = my (p=1); fordiv (n, d, p*=(1+'X^d)); vecmax(Vec(p))

Crossrefs

Cf. A000005, A027750.

Sequence in context: A340827 A360119 A033630 * A371213 A323719 A220122

Adjacent sequences: A308605 A308606 A308607 * A308609 A308610 A308611

Keyword

nonn

Author

Rémy Sigrist, Jun 10 2019

Status

approved