A211221 - OEIS

A211221

For any partition of n consider the product of the sigma of each element. Sequence gives the maximum of such values.

1, 3, 4, 9, 12, 27, 36, 81, 108, 243, 324, 729, 972, 2187, 2916, 6561, 8748, 19683, 26244, 59049, 78732, 177147, 236196, 531441, 708588, 1594323, 2125764, 4782969, 6377292, 14348907, 19131876, 43046721, 57395628, 129140163, 172186884, 387420489, 516560652

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..37.

Index entries for linear recurrences with constant coefficients, signature (0,3).

FORMULA

For n>1, a(n) = 3^n/2 for n even and a(n) = 4*3^(n-3)/2 for n odd.

For n>3, a(n) = 3*a(n-2). G.f.: x*(1+3*x+x^2)/(1-3*x^2). [Colin Barker, Apr 18 2012]

Closed form: a(1)=1, then a(n) = 1/6*(7-(-1)^(n-2))*3^(1/4*(-1)^(n-2))*3^(1/2*(n-2))*27^(1/4) = 3^((2*n+(-1)^n-5)/4)*(7-(-1)^n)/2. [Paolo P. Lava, Apr 20 2012]

EXAMPLE

For n=21 the partition (2,2,2,2,2,2,2,2,2,3) gives sigma(2)^9*sigma(3)=3^9*4=78732 that is the maximum value that can be reached.

MAPLE

with(numtheory); with(combinat);

A211221:=proc(q)

local b, c, i, j, k, m, n, t;

for n from 1 to q do

k:=partition(n); b:=numbpart(n); m:=0;

for i from 1 to b do

c:=nops(k[i]); t:=1;

for j from 1 to c do t:=t*sigma(k[i][j]); od; if t>m then m:=t; fi; od;

print(m);