A185032 Initial term of first run of exactly n consecutive numbers with 3 distinct prime factors.

30, 230, 644, 1308, 2664, 6850, 10280, 39693, 44360, 48919, 218972, 534078, 2699915, 526095, 17233173, 127890362, 29138958036, 146216247221, 23671413563491, 36966736685739

Offset: 1

Author

Roger B. Eggleton, Jason Kimberley, and James A. MacDougall, Apr 12 2011

Keywords

• nonn
• fini
• more

Comments

The number of distinct prime factors is A001221.

If any following terms exist, they are greater than 10^13.

Eggleton and MacDougall show that there are no more than 59 terms in this sequence.

a(19) <= 7523987244435061. - Donovan Johnson, Jul 08 2013

a(21) > 2 * 10^15, if it exists. - Toshitaka Suzuki, Jun 23 2025

Examples

			a(14) < a(13) because the first run of 13 consecutive integers i with A001221(i)=3 is not a maximal run.
		

Links

• Roger B. Eggleton and James A. MacDougall, Consecutive integers with equally many principal divisors, Math. Mag. 81 (2008), 235-248.
• Roger B. Eggleton, Jason S. Kimberley, and James A. MacDougall, Principal divisor ranks of the first trillion positive integers, NOVA: The University of Newcastle’s Digital Research Repository (2009).

Crossrefs

Cf. A080569, A064709, and A185042.

Extensions

a(19)-a(20) from Toshitaka Suzuki, Mar 24 2025