cp's OEIS Frontend

A356066 Numbers with a prime index that is not a prime-power. Complement of A355743.

%I A356066 #6 Aug 01 2022 08:21:24
%S A356066 2,4,6,8,10,12,13,14,16,18,20,22,24,26,28,29,30,32,34,36,37,38,39,40,
%T A356066 42,43,44,46,47,48,50,52,54,56,58,60,61,62,64,65,66,68,70,71,72,73,74,
%U A356066 76,78,79,80,82,84,86,87,88,89,90,91,92,94,96,98,100,101
%N A356066 Numbers with a prime index that is not a prime-power. Complement of A355743.
%C A356066 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 A356066 Union of A299174 and A356064.
%e A356066 The terms together with their prime indices begin:
%e A356066     2: {1}
%e A356066     4: {1,1}
%e A356066     6: {1,2}
%e A356066     8: {1,1,1}
%e A356066    10: {1,3}
%e A356066    12: {1,1,2}
%e A356066    13: {6}
%e A356066    14: {1,4}
%e A356066    16: {1,1,1,1}
%e A356066    18: {1,2,2}
%e A356066    20: {1,1,3}
%e A356066    22: {1,5}
%e A356066    24: {1,1,1,2}
%t A356066 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A356066 Select[Range[100],!And@@PrimePowerQ/@primeMS[#]&]
%Y A356066 The complement is A355743, counted by A023894.
%Y A356066 The squarefree complement is A356065, counted by A054685.
%Y A356066 Allowing prime index 1 gives A356064, complement A302492.
%Y A356066 A000688 counts factorizations into prime-powers, strict A050361.
%Y A356066 A001222 counts prime-power divisors.
%Y A356066 A034699 gives the maximal prime-power divisor.
%Y A356066 A246655 lists the prime-powers (A000961 includes 1), towers A164336.
%Y A356066 A355742 chooses a prime-power divisor of each prime index.
%Y A356066 Cf. A076610, A085970, A106244, A302493, A302601, A330946, A354911.
%K A356066 nonn
%O A356066 1,1
%A A356066 _Gus Wiseman_, Jul 31 2022