A075026 Define a number k to occupy a divisor cavity if d(k-1) > d(k) < d(k+1) where d(k) is the number of divisors of k. Sequence gives composite numbers occupying a divisor cavity.

9, 25, 49, 51, 55, 65, 69, 77, 91, 111, 115, 121, 125, 129, 153, 155, 161, 169, 175, 183, 185, 187, 209, 221, 235, 237, 247, 249, 259, 265, 267, 274, 287, 289, 291, 295, 305, 309, 319, 321, 323, 329, 339, 341, 343, 351, 355, 361, 365, 369, 371, 377, 386, 391

Offset: 0

Author

Amarnath Murthy, Sep 02 2002

Keywords

• nonn

Crossrefs

Cf. A000005, A075025, A075027.

Programs

Maple

q:= k-> not isprime(k) and (d->
        d(k-1)>d(k) and d(k)Alois P. Heinz, Sep 28 2021

Mathematica

Select[Flatten[Position[Partition[DivisorSigma[0,Range[400]],3,1],?(#[[1]]> #[[2]]<#[[3]]&),1,Heads->False]]+1,CompositeQ] (* _Harvey P. Dale, Oct 23 2019 *)

Extensions

Corrected and extended by Jason Earls, Sep 04 2002