A088862 Smallest number with exactly n prime factors (possibly with repetitions) such that in binary representation the divisors >1 form a prefix code.

1, 2, 9, 125, 625, 3125, 15625, 78125, 9921875, 1260078125, 25937424601, 285311670611, 145223640340999, 21557022777501157, 799006685782884121, 15181127029874798299, 288441413567621167681, 5480386857784802185939

Offset: 1

Author

Reinhard Zumkeller, Nov 26 2003

Keywords

• nonn

Comments

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

Conjecture: the sequence is defined for all n.

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

Examples

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

Crossrefs

Cf. A090335, A090332.

Extensions

More terms from David Wasserman, Aug 24 2005