OFFSET
1,2
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
75 is the Heinz number of (3,3,2), which has even weight, so 75 belongs to the sequence.
Sequence of even-weight partitions begins: () (2) (1,1) (4) (2,2) (3,1) (2,1,1) (6) (1,1,1,1) (8) (4,2) (5,1) (3,3) (2,2,2) (4,1,1).
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])::odd do od; k
end:
seq(a(n), n=1..100); # Alois P. Heinz, May 22 2018
MATHEMATICA
Select[Range[200], EvenQ[Total[Cases[FactorInteger[#], {p_, k_}:>k*PrimePi[p]]]]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 23 2018
STATUS
approved