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A005237
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Numbers n such that n and n+1 have same number of divisors.
(Formerly M2068)
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24
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2, 14, 21, 26, 33, 34, 38, 44, 57, 75, 85, 86, 93, 94, 98, 104, 116, 118, 122, 133, 135, 141, 142, 145, 147, 158, 171, 177, 189, 201, 202, 205, 213, 214, 217, 218, 230, 231, 242, 243, 244, 253, 285, 296, 298, 301, 302, 326, 332, 334, 344, 374, 375, 381, 387
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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REFERENCES
| M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 840.
R. K. Guy, Unsolved Problems in Number Theory, B18.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Is a(n) asymptotic to c*n with 9<c<10 ? - Benoit Cloitre, Sep 07 2002
Let S = {(n, a(n): n is a positive integer < 2*10^5}, where a(n) is the above sequence. The best-fit (least squares) line through S has equation y = 9.63976 x - 1453.76. S is very linear: the square of the correlation coefficient of {n} and {a(n)} is about 0.999943. - Joseph L. Pe (joseph_l_pe(AT)hotmail.com), May 15 2003
I conjecture the contrary: the sequence is superlinear. Perhaps a(n) ~ n log log n. [Charles R Greathouse IV, Aug 17 2011]
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LINKS
| T. D. Noe, Table of n, a(n) for n = 1..1000
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
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MATHEMATICA
| f[n_]:=Length[Divisors[n]]; lst={}; Do[If[f[n]==f[n+1], AppendTo[lst, n]], {n, 7!}]; lst [From Vladimir Orlovsky, Dec 14 2009]
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PROG
| (PARI) for(n=1, 1e4, if(numdiv(n)==numdiv(n+1), print1(n", "))) \\ Charles R Greathouse IV, Aug 17 2011
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CROSSREFS
| Cf. A000005, A005238, A006601, A049051, A006558, A019273, A039665.
Equals A083795(n-1) - 1.
Sequence in context: A101398 A131221 A138047 * A140578 A052213 A086263
Adjacent sequences: A005234 A005235 A005236 * A005238 A005239 A005240
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Jud McCranie (JudMcCranie(AT)ugaalum.uga.edu) Oct 15 1997
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