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 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 Alois P. Heinz, Table of n, a(n) for n = 1..1000 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 Cf. A000203, A085884, A211217-A211219, A211221. Sequence in context: A014602 A078823 A045615 * A051201 A026449 A286904 Adjacent sequences: A211217 A211218 A211219 * A211221 A211222 A211223 KEYWORD nonn AUTHOR Paolo P. Lava, Apr 11 2012 EXTENSIONS Extended beyond a(47) by Alois P. Heinz, May 30 2013 STATUS approved

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