OFFSET
1,2
COMMENTS
The original definition was: Numbers n such that A066897(n) is an odd number.
The sequence A281708(n) = b(n) = Sum_{k=1..n} k^3 * p(k) * p(n-k) of Peter Bala appears to have the property that b(n)/n is a positive integer if n is odd, and b(2*n)/n is a positive integer which is odd iff n is a member of this sequence. - Michael Somos, Jan 28 2017
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
EXAMPLE
7 is in the sequence because the number of partitions of 7 is equal to 15 and both 7 and 15 are odd numbers. - Omar E. Pol, Mar 18 2012
MAPLE
# We conjecture the following program produces the sequence
with(combinat):
b := n -> add(k^3*numbpart(k)*numbpart(n-k), k = 1..n):
c := n -> 2( b(n)/n - floor(b(n)/n) ):
for n from 1 to 400 do
if c(n) = 1 then print(n/2) end if
end do;
# Peter Bala, Jan 26 2017
MATHEMATICA
Select[Range[1, 200, 2], OddQ[PartitionsP[#]] &] (* T. D. Noe, Mar 18 2012 *)
PROG
(PARI) isok(n) = (n % 2) && (numbpart(n) % 2); \\ Michel Marcus, Jan 26 2017
KEYWORD
easy,nonn
AUTHOR
Naohiro Nomoto, Jan 30 2002
EXTENSIONS
New name and more terms from Omar E. Pol, Mar 18 2012
STATUS
approved