A104169 Highly decomposable Smith numbers. A Smith number which sets a record for the number of prime factors (counting multiplicity) starting from first Smith number is called a highly decomposable Smith number.

4, 27, 378, 576, 2688, 17496, 44928, 75776, 168960, 319488, 958464, 2883584, 5767168, 7077888, 279969792, 544997376, 778567680, 2579496960, 3875536896, 22749904896, 60699967488, 87509958656, 164886478848, 199715979264, 446676598784, 2954937499648

Offset: 1

Author

Shyam Sunder Gupta, Mar 10 2005 and May 03 2005

Keywords

• nonn
• base

Comments

It is conjectured that except for 27, all highly decomposable Smith numbers are even.

a(27) > 1.286e13. - Max Alekseyev, Oct 03 2024

Examples

			a(3) = 378 because the Smith number 378 has 5 prime factors which is > any Smith number < 378.
		

References

• Shyam Sunder Gupta, Smith Numbers, Mathematical Spectrum, 37 (2004/5), 27-29.

Links

• Shyam Sunder Gupta, Smith Numbers.
• Shyam Sunder Gupta, Smith Numbers, Exploring the Beauty of Fascinating Numbers, Springer (2025), Ch. 4, 127-157.

Crossrefs

Subsequence of A104168.

Cf. A006753.

Formula

Number m = A104168(k) in this sequence iff m = min_{n>=k} A104168(n).

Extensions

a(20)-a(23) from Donovan Johnson, Jan 02 2013

a(24)-a(26) from Max Alekseyev, Sep 28 2024