A185042 Initial term of first run of exactly n consecutive numbers with 4 distinct prime factors.

210, 7314, 37960, 134043, 357642, 2713332, 1217250, 14273478, 44939642, 76067298, 163459742, 547163235, 2081479430, 2771263512, 11715712410, 17911205580, 56608713884, 203594236366, 118968284928, 2500769994070, 3157129230489, 22498525938216, 585927201062

Offset: 1

Author

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

Keywords

• nonn
• fini

Comments

The number of distinct prime factors is A001221.

a(23) = 585927201062; a(n) > 10^13 for n = 20, 21, 22, and n >= 24, if they exist.

Eggleton and MacDougall show that there are no more than 419 terms in this sequence.

a(28) > 2 * 10^15. - Toshitaka Suzuki, Jun 22 2025

Examples

			a(6) > a(7) because the first run of 6 consecutive integers i with A001221(i)=4 is not maximal.
		

Links

• Toshitaka Suzuki, Table of n, a(n) for n = 1..27
• 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. A064709, A185032, A087977.

Extensions

a(20)-a(22) from and a(23) added by Toshitaka Suzuki, Mar 24 2025