A359397 Squarefree numbers with weakly decreasing first differences of 0-prepended prime indices.

1, 2, 3, 5, 6, 7, 11, 13, 15, 17, 19, 21, 23, 29, 30, 31, 35, 37, 41, 43, 47, 53, 55, 59, 61, 65, 67, 71, 73, 77, 79, 83, 89, 91, 97, 101, 103, 105, 107, 109, 113, 119, 127, 131, 133, 137, 139, 143, 149, 151, 157, 163, 167, 173, 179, 181, 187, 191, 193, 197

Offset: 1

Author

Gus Wiseman, Dec 31 2022

Keywords

• nonn

Comments

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.

Examples

			715 has prime indices {3,5,6}, with first differences (2,1), which are weakly decreasing, so 715 is in the sequence.
		

Crossrefs

This is the squarefree case of A325362.

These are the sorted Heinz numbers of rows of A359361.

A005117 lists squarefree numbers.

A112798 lists prime indices, length A001222, sum A056239, reverse A296150.

A355536 lists first differences of prime indices, 0-prepended A287352.

A358136 lists partial sums of prime indices, row sums A318283.

Cf. A000009, A000720, A001221, A253566, A261079, A304818, A358137, A358169.

Programs

Mathematica

primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Select[Range[100],SquareFreeQ[#]&&GreaterEqual@@Differences[Prepend[primeMS[#],0]]&]

Formula

Intersection of A325362 and A005117.