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A006558
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Start of first run of n consecutive integers with same number of divisors.
(Formerly M2155)
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21
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OFFSET
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1,2
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COMMENTS
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a(10)<=14366256627859031643, a(11)<=193729158984658237901148, a(12)<=1284696910355238430481207644 - Bilgin Ali and Bruno Mishutka (bruno_mishutka(AT)hotmail.com), Dec 29 2006
a(10) <= 2642166652554075, a(11) <= 17707503256664346, a(12) <= 9827470582657267545. - David Wasserman, Feb 22 2008
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REFERENCES
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J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 33, pp 12, Ellipses, Paris 2008.
R. K. Guy "Unsolved Problems in Number Theory", section B18.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
David Wells, "The Penguin Dictionary of Curious and Interesting Numbers," Penguin Books, NY, 1986, pages 147 and 176.
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LINKS
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Table of n, a(n) for n=1..9.
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MAPLE
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with(numtheory); A006558:=proc(q, w) local a, k, j, ok, n;
for j from 0 to w do for n from 1 to q do ok:=1; a:=tau(n);
for k from 1 to j do if a<>tau(n+k) then ok:=0; break; fi; od;
if ok=1 then print(n); break; fi;
od; od; end: A006558(10^10, 20); # Paolo P. Lava, May 03 2013
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CROSSREFS
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Cf. A000005, A005237, A005238, A006601, A049051, A019273, A039665.
Cf. A034173, A115158.
Sequence in context: A156369 A128152 A052403 * A002561 A181547 A030448
Adjacent sequences: A006555 A006556 A006557 * A006559 A006560 A006561
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Robert G. Wilson v
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EXTENSIONS
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Jud McCranie points out that the entry 40311 given in Guy and Wells is incorrect.
a(8) from Jud McCranie, Jan 20 2002
a(9) <= 2197379769820 from David Wasserman, Jan 08 2006; a(9)=2197379769820 from Jud McCranie, Jan 14 2006.
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STATUS
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approved
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