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A185042 Initial term of first run of exactly n consecutive numbers with 4 distinct prime factors. 1
210, 7314, 37960, 134043, 357642, 2713332, 1217250, 14273478, 44939642, 76067298, 163459742, 547163235, 2081479430, 2771263512, 11715712410, 17911205580, 56608713884, 203594236366, 118968284928 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 23 14:15 EDT 2019. Contains 322386 sequences. (Running on oeis4.)