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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
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
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
Sequence in context: A257711 A061133 A087977 * A323963 A023905 A035840
KEYWORD
nonn,fini,more
AUTHOR
R. B. Eggleton, Jason Kimberley, and J. A. MacDougall, Apr 12 2011
STATUS
approved