A200722 - OEIS

%I #21 May 13 2013 01:54:21

%S 6,8,11,13,15,16,21,27,29,31,35,37,41,43,47,53,55,59,61,65,67,71,73,

%T 77,79,81,85,91,95,115,119,125,127,131,133,137,139,143,149,151,157,

%U 161,163,167,173,179,181,187,191,193,197,199,203,209,211,217,221,223

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

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

%H Charles R Greathouse IV, <a href="/A200722/b200722.txt">Table of n, a(n) for n = 1..10000</a>

%F 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.

%o (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)

%Y Cf. A135581.

%K nonn

%O 1,1

%A _Charles R Greathouse IV_, Nov 29 2011