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%I #10 Sep 28 2021 17:28:32
%S 9,25,49,51,55,65,69,77,91,111,115,121,125,129,153,155,161,169,175,
%T 183,185,187,209,221,235,237,247,249,259,265,267,274,287,289,291,295,
%U 305,309,319,321,323,329,339,341,343,351,355,361,365,369,371,377,386,391
%N 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.
%p q:= k-> not isprime(k) and (d->
%p d(k-1)>d(k) and d(k)<d(k+1))(numtheory[tau]):
%p select(q, [$1..400])[]; # _Alois P. Heinz_, Sep 28 2021
%t Select[Flatten[Position[Partition[DivisorSigma[0,Range[400]],3,1],_?(#[[1]]> #[[2]]<#[[3]]&),1,Heads->False]]+1,CompositeQ] (* _Harvey P. Dale_, Oct 23 2019 *)
%Y Cf. A000005, A075025, A075027.
%K nonn
%O 0,1
%A _Amarnath Murthy_, Sep 02 2002
%E Corrected and extended by _Jason Earls_, Sep 04 2002