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Smallest number with exactly n prime factors (possibly with repetitions) such that in binary representation the divisors >1 form a prefix code.
2

%I #6 Mar 31 2012 13:20:51

%S 1,2,9,125,625,3125,15625,78125,9921875,1260078125,25937424601,

%T 285311670611,145223640340999,21557022777501157,799006685782884121,

%U 15181127029874798299,288441413567621167681,5480386857784802185939

%N Smallest number with exactly n prime factors (possibly with repetitions) such that in binary representation the divisors >1 form a prefix code.

%C a(n) = Min{k: A090330(k)=0 and A001222(k)=n};

%C Conjecture: the sequence is defined for all n.

%C If a(n) = p^n, then for m > n, a(m) >= p^m. In particular, a(n) = 19^n for 13 < n < 86. - _David Wasserman_, Aug 24 2005

%e a(5) = 3125 = 5^5 with divisors >1: 5, 25, 125, 625, 3125, which are prefix-free in binary: 101, 11001, 1111101, 1001110001, 110000110101.

%Y Cf. A090335, A090332.

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, Nov 26 2003

%E More terms from _David Wasserman_, Aug 24 2005