OFFSET
1,2
COMMENTS
First differs from A301899 in having 70 and lacking 105.
First differs from A325398 in having 70.
First differs from A319315 in having 966.
The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
The differences of a sequence are defined as if the sequence were increasing, so for example the differences of (6,3,1) are (-3,-2).
The zeroth differences of a sequence are the sequence itself, while the k-th differences for k > 0 are the differences of the (k-1)-th differences.
The enumeration of these partitions by sum is given by A325468.
LINKS
EXAMPLE
The sequence of terms together with their prime indices begins:
1: {}
2: {1}
3: {2}
5: {3}
6: {1,2}
7: {4}
10: {1,3}
11: {5}
13: {6}
14: {1,4}
15: {2,3}
17: {7}
19: {8}
21: {2,4}
22: {1,5}
23: {9}
26: {1,6}
29: {10}
31: {11}
33: {2,5}
For example, the k-th differences for k = 0...3 of the partition (9,4,2,1) with Heinz number 966 are
9 4 2 1
-5 -2 -1
3 1
-2
and since the entries of each row are distinct, 966 belongs to the sequence.
MATHEMATICA
primeptn[n_]:=If[n==1, {}, Reverse[Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]];
Select[Range[100], And@@Table[UnsameQ@@Differences[primeptn[#], k], {k, 0, PrimeOmega[#]}]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 03 2019
STATUS
approved