OFFSET
0,5
COMMENTS
a(n) is also the sum of smallest parts of all partitions of n minus the sum of divisors of n, for n >= 1.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
FORMULA
EXAMPLE
For n = 6 the partitions of 6 are
6 ....................... all parts are equal.
5 + 1 ................... contains only one largest part.
4 + 2 ................... contains only one largest part.
4 + 1 + 1 ............... contains only one largest part.
3 + 3 ................... all parts are equal.
3 + 2 + 1 ............... contains only one largest part.
3 + 1 + 1 + 1 ........... contains only one largest part.
2 + 2 + 2 ............... all parts are equal.
2 + 2 + 1 + 1 ........... contains two largest parts.
2 + 1 + 1 + 1 + 1 ....... contains only one largest part.
1 + 1 + 1 + 1 + 1 + 1 ... all parts are equal.
There are 8 largest parts, so a(6) = 8.
MAPLE
b:= proc(n, i) option remember; `if`(n=i, n, 0)+
`if`(i<1, 0, b(n, i-1) +`if`(n<i, 0, b(n-i, i)))
end:
a:= n-> b(n, n) -numtheory[sigma](n):
seq(a(n), n=0..100); # Alois P. Heinz, Jan 17 2013
MATHEMATICA
b[n_, i_] := b[n, i] = If[n == i, n, 0] + If[i < 1, 0, b[n, i - 1] + If[n < i, 0, b[n - i, i]]]; a[n_] := b[n, n] - DivisorSigma[1, n]; a[0] = 0; Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Feb 06 2017, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Omar E. Pol, Jul 14 2011
EXTENSIONS
More terms a(13)-a(46) from David Scambler, Jul 15 2011
STATUS
approved