OFFSET
1,1
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 greater than that of their conjugate.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..2000
Richard Ehrenborg and Einar Steingrímsson, The Excedance Set of a Permutation, Advances in Applied Mathematics 24, (2000), 284-299.
MathOverflow, Why 'excedances' of permutations? [closed].
FORMULA
a(n) > A122111(a(n)).
EXAMPLE
The terms together with their prime indices begin:
4: (1,1)
8: (1,1,1)
12: (2,1,1)
16: (1,1,1,1)
18: (2,2,1)
24: (2,1,1,1)
27: (2,2,2)
32: (1,1,1,1,1)
36: (2,2,1,1)
40: (3,1,1,1)
48: (2,1,1,1,1)
50: (3,3,1)
54: (2,2,2,1)
60: (3,2,1,1)
64: (1,1,1,1,1,1)
For example, the partition (4,4,1,1) has Heinz number 196 and its conjugate (4,2,2,2) has Heinz number 189, and 196 > 189, so 196 is in the sequence, and 189 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