A083794 Numbers n such that tau(n) is different from tau(n-1), where tau(m) = number of divisors of m.

1, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 23, 24, 25, 26, 28, 29, 30, 31, 32, 33, 36, 37, 38, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 77, 78, 79, 80, 81, 82

Offset

1,2

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

P. Erdős, On a problem of Chowla and some related problems, Proc. Cambridge Philos. Soc. 32 (1936), pp. 530-540.

Formula

Erdős proved that a(n) ~ n. - Charles R Greathouse IV, Dec 05 2012

Maple

with(numtheory): for n from 1 to 150 do if tau(n) <> tau(n-1) then printf(`%d, `, n) fi: od: # James A. Sellers, May 19 2003

Mathematica

a083794[n_] :=
 Prepend[Select[Range[1, n],
DivisorSigma[0, #] != DivisorSigma[0, # - 1] &], 1]; a083794[82] (* Michael De Vlieger, Dec 24 2014 *)

Prog

(PARI) is(n)=numdiv(n-1)!=numdiv(n)

Crossrefs

Cf. A083795.

Sequence in context: A326178 A162880 A083792 * A133016 A026503 A235498

Adjacent sequences: A083791 A083792 A083793 * A083795 A083796 A083797

Keyword

nonn

Author

Amarnath Murthy, May 07 2003

Extensions

More terms from James A. Sellers, May 19 2003

Status

approved