A340768 Third-smallest divisor of n-th composite number.

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

Author

Charles Kusniec, Jan 20 2021

Keywords

• nonn
• easy

Comments

The terms are either primes or squares of primes.

Crossrefs

Cf. A020639, A000290, A000040, A002808, A001248, A000430.

Programs

Mathematica

f[n_] := Divisors[n][[3]]; f /@ Select[Range[100], CompositeQ] (* Amiram Eldar, Jan 20 2021 *)

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