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

1, 6, 12, 24, 30, 48, 60, 72, 120, 144, 180, 192, 210, 288, 360, 384, 432, 480, 576, 720, 768, 840, 864, 900, 1080, 1152, 1260, 1296, 1440, 1680, 1728, 1920, 2160, 2304, 2520, 2592, 2880, 3072, 3360, 4320, 4608, 4620, 5040, 5400, 6300, 6912, 7200, 7560, 7680

Offset

1,2

Comments

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.

Permutations of prime indices are counted by A008480.

Links

Table of n, a(n) for n=1..49.

Example

The terms together with their prime indices begin:
      1: {}
      6: {1,2}
     12: {1,1,2}
     24: {1,1,1,2}
     30: {1,2,3}
     48: {1,1,1,1,2}
     60: {1,1,2,3}
     72: {1,1,1,2,2}
    120: {1,1,1,2,3}
    144: {1,1,1,1,2,2}
    180: {1,1,2,2,3}
    192: {1,1,1,1,1,1,2}
    210: {1,2,3,4}
    288: {1,1,1,1,1,2,2}
    360: {1,1,1,2,2,3}
    384: {1,1,1,1,1,1,1,2}
    432: {1,1,1,1,2,2,2}
    480: {1,1,1,1,1,2,3}

Mathematica

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
fir[q_]:=Select[Range[Length[q]], !MemberQ[Take[q, #-1], q[[#]]]&];
fir[Table[Length[Permutations[primeMS[n]]], {n, 1000}]]

Crossrefs

Sorted list of positions of first appearances in A008480.

The unsorted version is A304938.

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

A289509 lists numbers with relatively prime prime indices.

A344606 counts alternating permutations of prime indices.

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

Sequence in context: A119840 A298033 A358507 * A069171 A071611 A216453

Adjacent sequences: A358523 A358524 A358525 * A358527 A358528 A358529

Keyword

nonn

Author

Gus Wiseman, Nov 21 2022

Status

approved