cp's OEIS Frontend

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

%I A359397 #7 Jan 01 2023 19:30:36
%S A359397 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 A359397 65,67,71,73,77,79,83,89,91,97,101,103,105,107,109,113,119,127,131,
%U A359397 133,137,139,143,149,151,157,163,167,173,179,181,187,191,193,197
%N A359397 Squarefree numbers with weakly decreasing first differences of 0-prepended prime indices.
%C A359397 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 A359397 Intersection of A325362 and A005117.
%e A359397 715 has prime indices {3,5,6}, with first differences (2,1), which are weakly decreasing, so 715 is in the sequence.
%t A359397 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A359397 Select[Range[100],SquareFreeQ[#]&&GreaterEqual@@Differences[Prepend[primeMS[#],0]]&]
%Y A359397 This is the squarefree case of A325362.
%Y A359397 These are the sorted Heinz numbers of rows of A359361.
%Y A359397 A005117 lists squarefree numbers.
%Y A359397 A112798 lists prime indices, length A001222, sum A056239, reverse A296150.
%Y A359397 A355536 lists first differences of prime indices, 0-prepended A287352.
%Y A359397 A358136 lists partial sums of prime indices, row sums A318283.
%Y A359397 Cf. A000009, A000720, A001221, A253566, A261079, A304818, A358137, A358169.
%K A359397 nonn
%O A359397 1,2
%A A359397 _Gus Wiseman_, Dec 31 2022