

A200722


Numbers that are the 5thsmallest divisor of n for some n with precisely 25 divisors.


2



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
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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]==3f[1, 2]==4(f[1, 2]==1&&(f[1, 1]>126(f[1, 1]<80&&f[1, 1]>28)f[1, 1]==11f[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: A309627 A085412 A228650 * A120152 A315855 A287408
Adjacent sequences: A200719 A200720 A200721 * A200723 A200724 A200725


KEYWORD

nonn


AUTHOR

Charles R Greathouse IV, Nov 29 2011


STATUS

approved



