The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A211220 For any partition of n consider the sum of the sigma of each element. Sequence gives the maximum of such values. 2
1, 3, 4, 7, 8, 12, 13, 15, 16, 19, 20, 28, 29, 31, 32, 35, 36, 40, 41, 43, 44, 47, 48, 60, 61, 63, 64, 67, 68, 72, 73, 75, 76, 79, 80, 91, 92, 94, 95, 98, 99, 103, 104, 106, 107, 110, 111, 124, 125, 127, 128, 131, 132, 136, 137, 139, 140, 143, 144, 168, 169 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
For n equal to 1, 2, 3, 4, 6, 8, 12, 24, 30, 36, etc. the maximum value is equal to sigma(n).
LINKS
EXAMPLE
For n=10 the partition (4,6) gives sigma(4)+sigma(6)= 7 + 12 = 19 that is the maximum value that can be reached.
For n=21 the partitions (1,8,12), (3,6,12) and (1,2,6,12) give:
sigma(1)+sigma(8)+sigma(12)= 1 + 15 + 28 = 44;
sigma(3)+sigma(6)+sigma(12)= 4 + 12 + 28 = 44;
sigma(1)+sigma(2)+ sigma(6)+sigma(12)= 1 + 3 + 12 + 28 = 44
that is the maximum value that can be reached.
MAPLE
with(numtheory); with(combinat);
A211220:=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:=0;
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:
A211220(100);
# second Maple program:
with(numtheory):
b:= proc(n, i) option remember; `if`(n=0, 0, `if`(i<1,
-infinity, max(seq(sigma(i)*j+b(n-i*j, i-1), j=0..n/i))))
end:
a:= n-> b(n$2):
seq(a(n), n=1..70); # Alois P. Heinz, May 30 2013
MATHEMATICA
b[n_, i_] := b[n, i] = If[n==0, 0, If[i<1, -Infinity, Max[Table[ DivisorSigma[1, i]*j + b[n-i*j, i-1], {j, 0, n/i}]]]]; a[n_] := b[n, n]; Table[a[n], {n, 1, 70}] (* Jean-François Alcover, Feb 16 2017, after Alois P. Heinz *)
CROSSREFS
Sequence in context: A014602 A078823 A045615 * A051201 A026449 A286904
KEYWORD
nonn
AUTHOR
Paolo P. Lava, Apr 11 2012
EXTENSIONS
Extended beyond a(47) by Alois P. Heinz, May 30 2013
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 30 04:46 EDT 2024. Contains 372958 sequences. (Running on oeis4.)