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A067567 Odd numbers with an odd number of partitions. 9
1, 3, 5, 7, 13, 17, 23, 29, 33, 35, 37, 39, 41, 43, 49, 51, 53, 61, 63, 67, 69, 71, 73, 77, 81, 83, 85, 87, 89, 91, 93, 95, 99, 105, 107, 111, 115, 119, 121, 123, 127, 139, 143, 145, 155, 157, 159, 161, 165, 169, 173, 177, 181, 183, 185, 189, 193, 195, 199 (list; graph; refs; listen; history; text; internal format)
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
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
CROSSREFS
Sequence in context: A304122 A032397 A028879 * A104294 A262100 A171566
KEYWORD
easy,nonn
AUTHOR
Naohiro Nomoto, Jan 30 2002
EXTENSIONS
New name and more terms from Omar E. Pol, Mar 18 2012
STATUS
approved

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Last modified March 29 01:36 EDT 2024. Contains 371264 sequences. (Running on oeis4.)