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A239054
Maximum of the partition function on the set of all partitions of n.
1
1, 2, 3, 5, 7, 11, 15, 25, 35, 55, 77, 125, 175, 275, 385, 625, 875, 1375, 1925, 3125, 4375, 6875, 9625, 15625, 21875, 34375, 48125, 78125, 109375, 171875, 240625, 390625, 546875, 859375, 1203125, 1953125, 2734375, 4296875, 6015625, 9765625
OFFSET
1,2
COMMENTS
Sequence taken from the Bessenrodt-Ono paper, page 4, table 2, column of maxp(n), n = 1..14.
For the precise definition of maxp(n) see the theorem 1.1 in the mentioned paper, pages 1-2.
First differs from A000041 at a(8).
LINKS
Christine Bessenrodt and Ken Ono, Maximal multiplicative properties of partitions, arXiv:1403.3352 [math.CO], 2014.
FORMULA
a(n) = A000041(n), if 1 <= n <= 7.
a(n) = 5^(n/4), if n is congruent to 0 {mod 4} and n >= 8.
a(n) = 7*5^((n-5)/4), if n is congruent to 1 {mod 4} and n >= 8.
a(n) = 11*5^((n-6)/4), if n is congruent to 2 {mod 4} and n >= 8.
a(n) = 11*7*5^((n-11)/4), if n is congruent to 3 {mod 4} and n >= 8.
MATHEMATICA
a[n_] := If[n <= 7, PartitionsP[n], Switch[Mod[n, 4], 0, 5^(n/4), 1, 7*5^((n-5)/4), 2, 11*5^((n-6)/4), 3, 11*7*5^((n-11)/4)]];
Array[a, 40] (* Jean-François Alcover, Sep 23 2018 *)
PROG
(PARI) a(n) = {if (n <= 7, numbpart(n), my(nmf = n % 4); if (nmf == 0, 5^(n/4), if (nmf == 1, 7*5^((n-5)/4), if (nmf == 2, 11*5^((n-6)/4), 11*7*5^((n-11)/4)); ); ); ); } \\ Michel Marcus, Mar 16 2014
CROSSREFS
Sequence in context: A177485 A218023 A165801 * A241725 A022480 A308927
KEYWORD
nonn
AUTHOR
Omar E. Pol, Mar 15 2014
EXTENSIONS
a(22) corrected by Michel Marcus, Jun 14 2022
STATUS
approved