A074827 Numbers n such that tau(n) > tau(n+1) where tau(x) = A000005(x).

4, 6, 8, 10, 12, 16, 18, 20, 22, 24, 28, 30, 32, 36, 40, 42, 45, 46, 48, 50, 52, 54, 56, 58, 60, 64, 66, 68, 70, 72, 76, 78, 80, 81, 82, 84, 88, 90, 92, 96, 100, 102, 105, 106, 108, 110, 112, 114, 117, 120, 124, 126, 128, 130, 132, 136, 138, 140, 144, 148, 150, 152

Offset: 1

Author

Donald S. McDonald, Sep 04 2002

Keywords

• nonn

Comments

The sequence of n such that tau(n)Benoit Cloitre, Sep 07 2002

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.

Crossrefs

Cf. A074775 (tau(n)

Programs

Mathematica

Select[Range@ 152, DivisorSigma[0, #] > DivisorSigma[0, # + 1] &] (* Michael De Vlieger, Jul 03 2015 *)
Position[Partition[DivisorSigma[0,Range[200]],2,1],?(#[[1]]>#[[2]]&),{1},Heads->False]//Flatten (* _Harvey P. Dale, Jan 17 2017 *)

PARI

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

Formula

a(n) seems to be asymptotic to d*n with d=2.2... - Benoit Cloitre, Sep 07 2002

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

Extensions

Corrected and extended by Robert G. Wilson v, Sep 06 2002

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