cp's OEIS Frontend

A358526 Numbers k whose prime indices have a different number of permutations than any number less than k.

%I A358526 #7 Nov 21 2022 22:01:45
%S A358526 1,6,12,24,30,48,60,72,120,144,180,192,210,288,360,384,432,480,576,
%T A358526 720,768,840,864,900,1080,1152,1260,1296,1440,1680,1728,1920,2160,
%U A358526 2304,2520,2592,2880,3072,3360,4320,4608,4620,5040,5400,6300,6912,7200,7560,7680
%N A358526 Numbers k whose prime indices have a different number of permutations than any number less than k.
%C A358526 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.
%C A358526 Permutations of prime indices are counted by A008480.
%e A358526 The terms together with their prime indices begin:
%e A358526       1: {}
%e A358526       6: {1,2}
%e A358526      12: {1,1,2}
%e A358526      24: {1,1,1,2}
%e A358526      30: {1,2,3}
%e A358526      48: {1,1,1,1,2}
%e A358526      60: {1,1,2,3}
%e A358526      72: {1,1,1,2,2}
%e A358526     120: {1,1,1,2,3}
%e A358526     144: {1,1,1,1,2,2}
%e A358526     180: {1,1,2,2,3}
%e A358526     192: {1,1,1,1,1,1,2}
%e A358526     210: {1,2,3,4}
%e A358526     288: {1,1,1,1,1,2,2}
%e A358526     360: {1,1,1,2,2,3}
%e A358526     384: {1,1,1,1,1,1,1,2}
%e A358526     432: {1,1,1,1,2,2,2}
%e A358526     480: {1,1,1,1,1,2,3}
%t A358526 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A358526 fir[q_]:=Select[Range[Length[q]],!MemberQ[Take[q,#-1],q[[#]]]&];
%t A358526 fir[Table[Length[Permutations[primeMS[n]]],{n,1000}]]
%Y A358526 Sorted list of positions of first appearances in A008480.
%Y A358526 The unsorted version is A304938.
%Y A358526 A056239 adds up prime indices, row sums of A112798, counted by A001222.
%Y A358526 A289509 lists numbers with relatively prime prime indices.
%Y A358526 A344606 counts alternating permutations of prime indices.
%Y A358526 Cf. A000040, A000720, A001221, A003963, A061395, A316524.
%K A358526 nonn
%O A358526 1,2
%A A358526 _Gus Wiseman_, Nov 21 2022