OFFSET
1,1
COMMENTS
The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..10000
EXAMPLE
15 is the Heinz number of (3,2), which has odd weight, so 15 belongs to the sequence.
Sequence of odd-weight partitions begins: (1) (3) (2,1) (1,1,1) (5) (4,1) (3,2) (7) (2,2,1) (3,1,1) (9) (2,1,1,1) (6,1).
MAPLE
a:= proc(n) option remember; local k; for k from 1+
`if`(n=1, 0, a(n-1)) while add(numtheory[pi]
(i[1])*i[2], i=ifactors(k)[2])::even do od; k
end:
seq(a(n), n=1..100); # Alois P. Heinz, May 22 2018
MATHEMATICA
Select[Range[200], OddQ[Total[Cases[FactorInteger[#], {p_, k_}:>k*PrimePi[p]]]]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 23 2018
STATUS
approved