A322030 Numbers whose prime factors all have the same order of primeness.

1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 14, 16, 17, 19, 23, 25, 26, 27, 28, 29, 31, 32, 37, 38, 41, 43, 46, 47, 49, 51, 52, 53, 56, 58, 59, 61, 64, 67, 71, 73, 74, 76, 79, 81, 83, 86, 89, 91, 92, 94, 97, 98, 101, 103, 104, 106, 107, 109, 112, 113, 116, 121, 122, 123

Offset

1,2

Comments

The order of primeness (A078442) of a prime number p is the number of times one must apply A000720 to obtain a nonprime number.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..20000

N. Fernandez, An order of primeness, F(p)

N. Fernandez, An order of primeness [cached copy, included at A006450 with permission of the author]

Example

182 is in the sequence because its prime factors 2, 7, 13 all have order of primeness 1.

Maple

with(numtheory):
p:= proc(n) option remember;
      `if`(isprime(n), 1+p(pi(n)), 0)
    end:
a:= proc(n) option remember; local k; for k from 1+`if`(n=1,
      0, a(n-1)) while nops(map(p, factorset(k)))>1 do od; k
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Nov 24 2018

Mathematica

ordpri[n_]:=If[!PrimeQ[n], 0, Length[NestWhileList[PrimePi, PrimePi[n], PrimeQ]]];
Select[Range[200], SameQ@@ordpri/@FactorInteger[#][[All, 1]]&]

Crossrefs

Cf. A000720, A006450, A007097, A007821, A049076, A076610, A078442, A109082, A114537, A184155, A276625, A322027, A322028.

Sequence in context: A212289 A191840 A214981 * A326623 A210576 A191848

Adjacent sequences: A322027 A322028 A322029 * A322031 A322032 A322033

Keyword

nonn

Author

Gus Wiseman, Nov 24 2018

Status

approved