OFFSET
1,2
COMMENTS
First differs from A109427 in lacking 54.
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 A325354.
LINKS
EXAMPLE
Most small numbers are in the sequence. However, the sequence of non-terms together with their prime indices begins:
18: {1,2,2}
36: {1,1,2,2}
50: {1,3,3}
54: {1,2,2,2}
60: {1,1,2,3}
70: {1,3,4}
72: {1,1,1,2,2}
75: {2,3,3}
90: {1,2,2,3}
98: {1,4,4}
100: {1,1,3,3}
108: {1,1,2,2,2}
120: {1,1,1,2,3}
126: {1,2,2,4}
140: {1,1,3,4}
144: {1,1,1,1,2,2}
147: {2,4,4}
150: {1,2,3,3}
154: {1,4,5}
162: {1,2,2,2,2}
MATHEMATICA
primeptn[n_]:=If[n==1, {}, Reverse[Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]];
Select[Range[100], And@@Table[Greater@@Differences[primeptn[#], k], {k, 0, PrimeOmega[#]}]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 02 2019
STATUS
approved