A200722 Numbers that are the 5th-smallest divisor of n for some n with precisely 25 divisors.

6, 8, 11, 13, 15, 16, 21, 27, 29, 31, 35, 37, 41, 43, 47, 53, 55, 59, 61, 65, 67, 71, 73, 77, 79, 81, 85, 91, 95, 115, 119, 125, 127, 131, 133, 137, 139, 143, 149, 151, 157, 161, 163, 167, 173, 179, 181, 187, 191, 193, 197, 199, 203, 209, 211, 217, 221, 223

Offset: 1

Author

Charles R Greathouse IV, Nov 29 2011

Keywords

• nonn

Comments

Members of A135581, sorted. Characterizations (see Formulas section, below) are possible for similar sequences as well.

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A135581.

Programs

PARI

is(n)=my(f=factor(n));if(#f[,1]==1,f[1,2]==3||f[1,2]==4||(f[1,2]==1&&(f[1,1]>126||(f[1,1]<80&&f[1,1]>28)||f[1,1]==11||f[1,1]==13)),#f[,1]==2&&f[1,2]==1&&f[2,2]==1&&f[2,1]
				

Formula

Characterization: all terms of this sequence are of the form p, p^3, p^4, or pq where p and q are distinct primes. All but 16 primes {2, 3, 5, 7, 17, 19, 23, 83, 89, 97, 101, 103, 107, 109, 113} are in this sequence; all p^3 and p^4 are in this sequence; pq is in this sequence for all p < q < p^2.