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

Offset

1,1

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.

Links

Table of n, a(n) for n=1..19.

Roger B. Eggleton and James A. MacDougall, Consecutive integers with equally many principal divisors, Math. Mag. 81 (2008), 235-248.

R. B. Eggleton, J. S. Kimberley, and J. A. MacDougall, Principal divisor ranks of the first trillion positive integers, NOVA: The University of Newcastle’s Digital Research Repository (2009).

Example

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

Crossrefs

Cf. A064709, A185032, and A087977.

Sequence in context: A257711 A061133 A087977 * A323963 A023905 A035840

Adjacent sequences: A185039 A185040 A185041 * A185043 A185044 A185045

Keyword

nonn,fini,more

Author

R. B. Eggleton, Jason Kimberley, and J. A. MacDougall, Apr 12 2011

Status

approved