A005238 Numbers k such that k, k+1 and k+2 have the same number of divisors.

33, 85, 93, 141, 201, 213, 217, 230, 242, 243, 301, 374, 393, 445, 603, 633, 663, 697, 902, 921, 1041, 1105, 1137, 1261, 1274, 1309, 1334, 1345, 1401, 1641, 1761, 1832, 1837, 1885, 1893, 1924, 1941, 1981, 2013, 2054, 2101, 2133, 2181, 2217, 2264, 2305

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• nice

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.
• J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 33, pp. 12, Ellipses, Paris 2008.
• 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).

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)
• 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].

Crossrefs

Cf. A000005, A005237, A006601, A049051, A006558, A019273, A039665, A051950.

Programs

Haskell

import Data.List (elemIndices)
a005238 n = a005238_list !! (n-1)
a005238_list = map (+ 1) $ elemIndices 0 $ zipWith (+) ds $ tail ds where
   ds = map abs $ zipWith (-) (tail a000005_list) a000005_list
-- Reinhard Zumkeller, Oct 03 2012

Mathematica

Select[Range[2500],DivisorSigma[0,#]==DivisorSigma[0,#+1] == DivisorSigma[ 0,#+2]&] (* Harvey P. Dale, Nov 12 2012 *)
Flatten[Position[Partition[DivisorSigma[0,Range[2500]],3,1],{x_,x_,x_}]] (* Harvey P. Dale, Jul 06 2015 *)
SequencePosition[DivisorSigma[0,Range[2500]],{x_,x_,x_}][[All,1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 03 2017 *)

PARI

is(n)=my(d=numdiv(n)); numdiv(n+1)==d && numdiv(n+2)==d \\ Charles R Greathouse IV, Feb 06 2017

Extensions

More terms from Olivier Gérard