OFFSET
1,1
COMMENTS
First differs from A212164 in lacking 72.
First differs from A293243 in lacking 72.
No terms are squarefree.
Also Heinz numbers of inseparable partitions (A325535). The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
These are also numbers that can be written as a product of prime numbers, each different from the last but not necessarily different from those prior to the last.
A multiset is inseparable iff its maximal multiplicity is greater than one plus the sum of its remaining multiplicities.
EXAMPLE
The sequence of terms together with their prime indices begins:
4: {1,1}
8: {1,1,1}
9: {2,2}
16: {1,1,1,1}
24: {1,1,1,2}
25: {3,3}
27: {2,2,2}
32: {1,1,1,1,1}
40: {1,1,1,3}
48: {1,1,1,1,2}
49: {4,4}
54: {1,2,2,2}
56: {1,1,1,4}
64: {1,1,1,1,1,1}
80: {1,1,1,1,3}
81: {2,2,2,2}
88: {1,1,1,5}
96: {1,1,1,1,1,2}
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], Select[Permutations[primeMS[#]], !MatchQ[#, {___, x_, x_, ___}]&]=={}&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 21 2020
STATUS
approved