A074775 Numbers n such that tau(n) < tau(n+1) where tau(x)=A000005(x).

1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 23, 25, 27, 29, 31, 35, 37, 39, 41, 43, 47, 49, 51, 53, 55, 59, 61, 62, 63, 65, 67, 69, 71, 73, 74, 77, 79, 83, 87, 89, 91, 95, 97, 99, 101, 103, 107, 109, 111, 113, 115, 119, 121, 123, 125, 127, 129, 131, 134, 137, 139, 143, 146, 149

Offset: 1

Author

Benoit Cloitre, Sep 07 2002

Keywords

• nonn

Links

• Charles R Greathouse IV, 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.
• Vaclav Kotesovec, Plot of a(n)/n for n = 1..5000000

Programs

Mathematica

Select[Range[1, 150], DivisorSigma[0,#] < DivisorSigma[0,#+1]&] (* Vaclav Kotesovec, Feb 16 2019 *)

PARI

is(n)=numdiv(n) < numdiv(n+1) \\ Charles R Greathouse IV, Dec 05 2012

Formula

a(n) seems to be asymptotic to c*n with c=2.23...

In fact, Erdős proved that a(n) ~ 2n. - Charles R Greathouse IV, Dec 05 2012