A359397 - OEIS

%I #7 Jan 01 2023 19:30:36

%S 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,

%T 65,67,71,73,77,79,83,89,91,97,101,103,105,107,109,113,119,127,131,

%U 133,137,139,143,149,151,157,163,167,173,179,181,187,191,193,197

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

%C 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.

%F Intersection of A325362 and A005117.

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

%t primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];

%t Select[Range[100],SquareFreeQ[#]&&GreaterEqual@@Differences[Prepend[primeMS[#],0]]&]

%Y This is the squarefree case of A325362.

%Y These are the sorted Heinz numbers of rows of A359361.

%Y A005117 lists squarefree numbers.

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

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

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

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

%K nonn

%O 1,2

%A _Gus Wiseman_, Dec 31 2022