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A322030
Numbers whose prime factors all have the same order of primeness.
3
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
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]]&]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 24 2018
STATUS
approved