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

0,1

Links

Table of n, a(n) for n=0..53.

Maple

q:= k-> not isprime(k) and (d->
        d(k-1)>d(k) and d(k)<d(k+1))(numtheory[tau]):
select(q, [$1..400])[];  # 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 *)

Crossrefs

Cf. A000005, A075025, A075027.

Sequence in context: A291259 A051132 A247687 * A339727 A339128 A113659

Adjacent sequences: A075023 A075024 A075025 * A075027 A075028 A075029

Keyword

nonn

Author

Amarnath Murthy, Sep 02 2002

Extensions

Corrected and extended by Jason Earls, Sep 04 2002

Status

approved