cp's OEIS Frontend

A353742 Sorted prime metasignature of n.

%I A353742 #11 Aug 02 2022 22:03:00
%S A353742 1,1,1,1,2,1,1,1,2,1,1,1,1,2,2,1,1,1,1,1,1,1,2,2,1,1,1,1,2,1,1,1,1,3,
%T A353742 1,1,2,2,2,2,1,2,2,1,1,1,3,1,1,1,1,1,2,1,1,1,1,1,1,2,1,1,1,1,1,2,1,1,
%U A353742 2,2,1,1,2,1,2,1,1,1,2,3,1,1,1,2,3,1,1
%N A353742 Sorted prime metasignature of n.
%C A353742 The prime metasignature counts the multiplicities of each value in the prime signature of n. For example, 2520 has prime indices {1,1,1,2,2,3,4}, sorted prime signature {1,1,2,3}, and sorted prime metasignature {1,1,2}.
%e A353742 The prime indices, sorted prime signatures, and sorted prime metasignatures of selected n:
%e A353742       n = 1: {}             -> {}         -> {}
%e A353742       n = 2: {1}            -> {1}        -> {1}
%e A353742       n = 6: {1,2}          -> {1,1}      -> {2}
%e A353742      n = 12: {1,1,2}        -> {1,2}      -> {1,1}
%e A353742      n = 30: {1,2,3}        -> {1,1,1}    -> {3}
%e A353742      n = 60: {1,1,2,3}      -> {1,1,2}    -> {1,2}
%e A353742     n = 210: {1,2,3,4}      -> {1,1,1,1}  -> {4}
%e A353742     n = 360: {1,1,1,2,2,3}  -> {1,2,3}    -> {1,1,1}
%t A353742 Join@@Table[Sort[Length/@Split[Sort[Last/@If[n==1,{},FactorInteger[n]]]]],{n,100}]
%Y A353742 Row-sums are A001221.
%Y A353742 Row-lengths are A071625.
%Y A353742 Positions of first appearances are A182863.
%Y A353742 This is the sorted version of A238747.
%Y A353742 Row-products are A353507.
%Y A353742 A001222 counts prime factors with multiplicity.
%Y A353742 A003963 gives product of prime indices.
%Y A353742 A005361 gives product of prime signature, firsts A353500 (sorted A085629).
%Y A353742 A056239 adds up prime indices, row sums of A112798 and A296150.
%Y A353742 A124010 gives prime signature, sorted A118914.
%Y A353742 A130091 lists numbers with strict signature, counted by A098859.
%Y A353742 A181819 gives prime shadow, with an inverse A181821.
%Y A353742 Cf. A000040, A000720, A070175, A097318, A182850, A304678, A325238, A353503.
%K A353742 nonn,tabf
%O A353742 1,5
%A A353742 _Gus Wiseman_, May 20 2022