A083794 Numbers k such that tau(k) is different from tau(k-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

Author

Amarnath Murthy, May 07 2003

Keywords

• nonn

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.

Crossrefs

Cf. A083795.

Programs

Maple

with(numtheory): for n from 1 to 150 do if tau(n) <> tau(n-1) then printf(`%d,`,n) fi: od: # James 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 *)

PARI

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

Formula

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

Extensions

More terms from James Sellers, May 19 2003