A358526 - OEIS

%I #7 Nov 21 2022 22:01:45

%S 1,6,12,24,30,48,60,72,120,144,180,192,210,288,360,384,432,480,576,

%T 720,768,840,864,900,1080,1152,1260,1296,1440,1680,1728,1920,2160,

%U 2304,2520,2592,2880,3072,3360,4320,4608,4620,5040,5400,6300,6912,7200,7560,7680

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

%C 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 Permutations of prime indices are counted by A008480.

%e The terms together with their prime indices begin:

%e       1: {}

%e       6: {1,2}

%e      12: {1,1,2}

%e      24: {1,1,1,2}

%e      30: {1,2,3}

%e      48: {1,1,1,1,2}

%e      60: {1,1,2,3}

%e      72: {1,1,1,2,2}

%e     120: {1,1,1,2,3}

%e     144: {1,1,1,1,2,2}

%e     180: {1,1,2,2,3}

%e     192: {1,1,1,1,1,1,2}

%e     210: {1,2,3,4}

%e     288: {1,1,1,1,1,2,2}

%e     360: {1,1,1,2,2,3}

%e     384: {1,1,1,1,1,1,1,2}

%e     432: {1,1,1,1,2,2,2}

%e     480: {1,1,1,1,1,2,3}

%t primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];

%t fir[q_]:=Select[Range[Length[q]],!MemberQ[Take[q,#-1],q[[#]]]&];

%t fir[Table[Length[Permutations[primeMS[n]]],{n,1000}]]

%Y Sorted list of positions of first appearances in A008480.

%Y The unsorted version is A304938.

%Y A056239 adds up prime indices, row sums of A112798, counted by A001222.

%Y A289509 lists numbers with relatively prime prime indices.

%Y A344606 counts alternating permutations of prime indices.

%Y Cf. A000040, A000720, A001221, A003963, A061395, A316524.

%K nonn

%O 1,2

%A _Gus Wiseman_, Nov 21 2022