A300063 Heinz numbers of integer partitions of odd numbers.

2, 5, 6, 8, 11, 14, 15, 17, 18, 20, 23, 24, 26, 31, 32, 33, 35, 38, 41, 42, 44, 45, 47, 50, 51, 54, 56, 58, 59, 60, 65, 67, 68, 69, 72, 73, 74, 77, 78, 80, 83, 86, 92, 93, 95, 96, 97, 98, 99, 103, 104, 105, 106, 109, 110, 114, 119, 122, 123, 124, 125, 126, 127

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

Complement of A300061.

Cf. A000041, A000720, A001222, A056239, A063834, A112798, A215366, A296150, A299757, A300056, A300060, A304662.

Sequence in context: A059009 A214642 A026179 * A230902 A243680 A280381

Adjacent sequences: A300060 A300061 A300062 * A300064 A300065 A300066

Keyword

nonn

Author

Gus Wiseman, Feb 23 2018

Status

approved