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A340768
Third-smallest divisor of n-th composite number.
1
4, 3, 4, 9, 5, 3, 7, 5, 4, 3, 4, 7, 11, 3, 25, 13, 9, 4, 3, 4, 11, 17, 7, 3, 19, 13, 4, 3, 4, 5, 23, 3, 49, 5, 17, 4, 3, 11, 4, 19, 29, 3, 31, 7, 4, 13, 3, 4, 23, 5, 3, 37, 5, 4, 11, 3, 4, 9, 41, 3, 17, 43, 29, 4, 3, 13, 4, 31, 47, 19, 3, 7, 9, 4, 3, 4, 5, 53
OFFSET
1,1
COMMENTS
The terms are either primes or squares of primes.
MATHEMATICA
f[n_] := Divisors[n][[3]]; f /@ Select[Range[100], CompositeQ] (* Amiram Eldar, Jan 20 2021 *)
PROG
(PARI) lista(nn)=my(list = List()); forcomposite(n=1, nn, listput(list, divisors(n)[3]); ); Vec(list); \\ Michel Marcus, Jan 20 2021
(PARI) do(lim)=my(v=List()); forfactored(n=4, lim\1, my(f=n[2]); if(#f~==1, if(f[1, 2]>1, listput(v, f[1, 1]^2)), listput(v, if(f[1, 2]>1, min(f[1, 1]^2, f[2, 1]), f[2, 1])))); Vec(v) \\ Charles R Greathouse IV, Nov 17 2022
(Python)
from sympy import divisors, composite
def A340768(n):
return divisors(composite(n))[2] # Chai Wah Wu, Jan 21 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Charles Kusniec, Jan 20 2021
STATUS
approved