OFFSET
1,2
COMMENTS
The Heinz number of a partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). The sequence lists all Heinz numbers of partitions whose Heinz number is less than or equal to that of their conjugate.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..10000
MathOverflow, Why 'excedances' of permutations? [closed].
Richard Ehrenborg and Einar Steingrímsson, The Excedance Set of a Permutation, Advances in Applied Mathematics 24, (2000), 284-299.
FORMULA
a(n) <= A122111(a(n)).
EXAMPLE
The terms together with their prime indices begin:
1: ()
2: (1)
3: (2)
5: (3)
6: (2,1)
7: (4)
9: (2,2)
10: (3,1)
11: (5)
13: (6)
14: (4,1)
15: (3,2)
17: (7)
19: (8)
20: (3,1,1)
For example, the partition (3,2,2) has Heinz number 45 and its conjugate (3,3,1) has Heinz number 50, and 45 <= 50, so 45 is in the sequence, and 50 is not.
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
conj[y_]:=If[Length[y]==0, y, Table[Length[Select[y, #>=k&]], {k, 1, Max[y]}]];
Select[Range[100], #<=Times@@Prime/@conj[primeMS[#]]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 20 2022
STATUS
approved