A106543 Composite numbers that are not perfect powers.

6, 10, 12, 14, 15, 18, 20, 21, 22, 24, 26, 28, 30, 33, 34, 35, 38, 39, 40, 42, 44, 45, 46, 48, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 102, 104, 105, 106

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) = n + O(n/log n). - Charles R Greathouse IV, Oct 03 2011

Maple

isA106543 := proc(n) local F; F := map(t -> t[2], ifactors(n)[2]); nops(F) > 1 and igcd(op(F)) = 1 end: select(isA106543, [$1..106]); # Peter Luschny, Oct 07 2025

Mathematica

perfPQ[n_]:=GCD@@FactorInteger[n][[All, 2]]>1; Select[Range[110], CompositeQ[ #] && !perfPQ[#]&] (* Harvey P. Dale, Oct 10 2017 *)

Prog

(PARI) lista(nn)=forcomposite(i=1, nn, if (! ispower(i), print1(i, ", ")); ); \\ Michel Marcus, Jun 27 2013
(PARI) is(n)=!isprime(n) && !ispower(n) && n>1 \\ Charles R Greathouse IV, Oct 19 2015
(SageMath)
def A106543_list(n) : return [k for k in (2..n) if not k.is_prime() and not k.is_perfect_power()]
A106543_list(106) # Terry D. Grant, Jul 17 2016
(Python)
from sympy import primepi, mobius, integer_nthroot
def A106543(n):
    def f(x): return int(n+1+primepi(x)-sum(mobius(k)*(integer_nthroot(x, k)[0]-1) for k in range(2, x.bit_length())))
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, Oct 12 2024

Crossrefs

Intersection of A002808 and A007916.

Cf. A105642, A089229.

Sequence in context: A335080 A323304 A325411 * A389065 A386207 A324455

Adjacent sequences: A106540 A106541 A106542 * A106544 A106545 A106546

Keyword

easy,nonn

Author

Alexandre Wajnberg, May 08 2005

Status

approved