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

1,1

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

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.

Prog

(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]<f[1, 1]^2)

Crossrefs

Cf. A135581.

Sequence in context: A085412 A228650 A358531 * A120152 A315855 A287408

Adjacent sequences: A200719 A200720 A200721 * A200723 A200724 A200725

Keyword

nonn

Author

Charles R Greathouse IV, Nov 29 2011

Status

approved