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Search: id:A002961
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| A002961 |
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Numbers n such that n and n+1 have same sum of divisors.
(Formerly M4950)
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+0
19
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| 14, 206, 957, 1334, 1364, 1634, 2685, 2974, 4364, 14841, 18873, 19358, 20145, 24957, 33998, 36566, 42818, 56564, 64665, 74918, 79826, 79833, 84134, 92685, 109214, 111506, 116937, 122073, 138237, 147454, 161001, 162602, 166934
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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For the values of n < 2*10^10 in this sequence, sigma(n)/n is between 1.5 and 2.25. - T. D. Noe, Sep 17 2007
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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.
W. Sierpi\'{n}ski, A Selection of Problems in the Theory of Numbers. Macmillan, NY, 1964, p. 110.
R. K. Guy, Unsolved Problems in Theory of Numbers, Sect. B13.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1378
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].
Lourdes Benito, Solutions of the problem of Erdos-Sierpinski: sigma(n)=sigma(n+1)
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MAPLE
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with(numtheory); P:=proc(n) local a, i; for i from 1 by 1 to n do a:=sigma(i)/sigma(i+1); if a=1 then print(i); fi; od; end: P(100000); - Paolo P. Lava (ppl(AT)spl.at), Aug 23 2007
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MATHEMATICA
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f[n_]:=DivisorSigma[1, n]; lst={}; Do[If[f[n]==f[n+1], AppendTo[lst, n]], {n, 9!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jul 22 2009]
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CROSSREFS
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A000203 (sigma function), A053215, A053249, A054004
Sequence in context: A068769 A113349 A109764 this_sequence A063071 A160682 A097261
Adjacent sequences: A002958 A002959 A002960 this_sequence A002962 A002963 A002964
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Mira Bernstein, Robert G. Wilson v (rgwv(AT)rgwv.com)
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EXTENSIONS
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More terms from Jud McCranie (j.mccranie(AT)comcast.net) Oct 15 1997
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