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Search: id:A087977
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| A087977 |
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a(n) is the first term in a chain of at least n consecutive numbers each having exactly four distinct prime factors. |
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+0
5
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| 210, 7314, 37960, 134043, 357642, 1217250, 1217250, 14273478, 44939642, 76067298, 163459742, 547163235, 2081479430, 2771263512, 11715712410, 17911205580, 56608713884, 118968284928, 118968284928, 585927201062
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Eggleton and MacDougall show that there are no more than 419 terms in this sequence. [From T. D. Noe (noe(AT)sspectra.com), Oct 13 2008]
a(24) > 10^13. [From Donovan Johnson (donovan.johnson(AT)yahoo.com), Jan 15 2009]
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REFERENCES
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Roger B. Eggleton and James A. MacDougall, Consecutive integers with equally many principal divisors, Math. Mag. 81 (2008), 235-248. [From T. D. Noe (noe(AT)sspectra.com), Oct 13 2008]
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LINKS
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Donovan Johnson, Table of n, a(n) for n=1..23
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EXAMPLE
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a(6)=a(7)=1217250 because the relevant 7 successive numbers have 4 distinct prime-factors: {[2.9.125.541], [7.17.53.193], [4.23.101.131], [3.47.89.97], [2.19.103.311], [5.13.61.307], [8.3.67.757]}.
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MATHEMATICA
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k=1; Do[While[Union[Table[Length[FactorInteger[i]], {i, k, k+n-1}]]!={4}, k++ ]; Print[k], {n, 1, 8}]
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CROSSREFS
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Cf. A080569[m=3], A064708[m=2].
Cf. A087978, A138206, A138207, A154573. [From Donovan Johnson (donovan.johnson(AT)yahoo.com), Jan 15 2009]
Sequence in context: A024449 A103604 A061133 this_sequence A023905 A035840 A140904
Adjacent sequences: A087974 A087975 A087976 this_sequence A087978 A087979 A087980
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Sep 26 2003
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EXTENSIONS
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More terms from Don Reble (djr(AT)nk.ca), Sep 29 2003
a(13)-a(19) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Mar 06 2008
a(20)-a(23) and b-file from Donovan Johnson (donovan.johnson(AT)yahoo.com), Jan 15 2009
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