OFFSET
0,4
COMMENTS
These are partitions of n whose length is an odd divisor of n.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1000
EXAMPLE
The a(1) = 1 through a(10) = 8 partitions (A = 10):
1 2 3 4 5 6 7 8 9 A
111 11111 222 1111111 333 22222
321 432 32221
411 441 33211
522 42211
531 43111
621 52111
711 61111
111111111
For example, the partition (3,3,2,1,1) has length 5 and mean 2, so is counted under a(10).
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], OddQ[Length[#]]&&IntegerQ[Mean[#]]&]], {n, 0, 30}]
PROG
(PARI) a(n)=if(n==0, 0, sumdiv(n, d, if(d%2, polcoef(1/prod(k=1, d, 1 - x^k + O(x^(n-d+1))), n-d)))) \\ Andrew Howroyd, Mar 24 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 24 2023
STATUS
approved