A075027 Numbers k such that d(k-1) < d(k) > d(k+1), d = A000005.

4, 6, 8, 10, 12, 16, 18, 20, 24, 28, 30, 32, 36, 40, 42, 48, 50, 52, 54, 56, 60, 64, 66, 68, 70, 72, 78, 80, 84, 88, 90, 92, 96, 100, 102, 108, 110, 112, 114, 120, 124, 126, 128, 130, 132, 138, 140, 144, 150, 152, 154, 156, 160, 162, 165, 168, 170, 174, 176, 180

Offset: 1

Author

Amarnath Murthy, Sep 02 2002

Keywords

• nonn

Comments

Obviously every term is composite.

The average of each twin prime pair is a term.

a(55) = 165 is the first odd term; A323379 lists all odd terms. - Jon E. Schoenfield, Sep 26 2021

Examples

			10 is a term since d(9) = 3, d(10) = 4, d(11) = 2 and 3 < 4 > 2.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..3403 (first 1001 terms from Harvey P. Dale)

Crossrefs

Cf. A000005, A014574, A075025, A075026, A323379.

Programs

Maple

q:= k-> (d-> d(k-1)d(k+1))(numtheory[tau]):
select(q, [$1..200])[];  # Alois P. Heinz, Sep 28 2021

Mathematica

#[[2,1]]&/@Select[Partition[Table[{n,DivisorSigma[0,n]},{n,200}],3,1], #[[1,-1]]<#[[2,-1]]>#[[3,-1]]&] (* Harvey P. Dale, Oct 09 2011 *)

Extensions

More terms from Jason Earls, Sep 04 2002