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A211221
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For any partition of n consider the product of the sigma of each element. Sequence gives the maximum of such values.
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3
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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
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1,2
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LINKS
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FORMULA
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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]
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EXAMPLE
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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.
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MAPLE
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with(numtheory); with(combinat);
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);
od; end:
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MATHEMATICA
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LinearRecurrence[{0, 3}, {1, 3, 4}, 40] (* Harvey P. Dale, Jun 06 2015 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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