cp's OEIS Frontend

A303945 Triangle whose n-th row lists the multiset of prime indices of the n-th number that is not a perfect power A007916(n).

%I A303945 #5 May 06 2018 12:43:25
%S A303945 1,2,3,1,2,4,1,3,5,1,1,2,6,1,4,2,3,7,1,2,2,8,1,1,3,2,4,1,5,9,1,1,1,2,
%T A303945 1,6,1,1,4,10,1,2,3,11,2,5,1,7,3,4,12,1,8,2,6,1,1,1,3,13,1,2,4,14,1,1,
%U A303945 5,2,2,3,1,9,15,1,1,1,1,2,1,3,3,2,7,1,1
%N A303945 Triangle whose n-th row lists the multiset of prime indices of the n-th number that is not a perfect power A007916(n).
%C A303945 A number is not a perfect power if its prime multiplicities are relatively prime. This triangle is an enumeration of all finite aperiodic multisets of positive integers, where a multiset is aperiodic if its multiplicities are relatively prime.
%e A303945 Sequence of numbers that are not perfect powers together with their multisets of prime indices begins:
%e A303945 2:  {1}
%e A303945 3:  {2}
%e A303945 5:  {3}
%e A303945 6:  {1,2}
%e A303945 7:  {4}
%e A303945 10: {1,3}
%e A303945 11: {5}
%e A303945 12: {1,1,2}
%e A303945 13: {6}
%e A303945 14: {1,4}
%e A303945 15: {2,3}
%e A303945 17: {7}
%e A303945 18: {1,2,2}
%e A303945 19: {8}
%e A303945 20: {1,1,3}
%e A303945 21: {2,4}
%e A303945 22: {1,5}
%e A303945 23: {9}
%e A303945 24: {1,1,1,2}
%e A303945 26: {1,6}
%e A303945 28: {1,1,4}
%e A303945 29: {10}
%e A303945 30: {1,2,3}
%t A303945 primeMS[n_]:=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A303945 primeMS/@Select[Range[2,100],GCD@@FactorInteger[#][[All,2]]===1&]
%Y A303945 Cf. A000041, A000720, A000837, A001222, A005117, A007916, A052409, A052410, A056239, A112798, A296150.
%K A303945 nonn,tabf
%O A303945 1,2
%A A303945 _Gus Wiseman_, May 03 2018