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A328510 Smallest number whose divisors have n non-singleton runs.

%I A328510 #12 Oct 27 2019 05:08:52
%S A328510 1,2,20,90,630,1260,3780,21420,41580,128520,270270,554400,706860,
%T A328510 1413720,2042040,4324320,4084080,9189180,6126120,43825320,12252240,
%U A328510 18378360,82162080,36756720,85765680,73513440,183783600,306306000,257297040,563603040,514594080
%N A328510 Smallest number whose divisors have n non-singleton runs.
%H A328510 Giovanni Resta, <a href="/A328510/b328510.txt">Table of n, a(n) for n = 0..54</a>
%e A328510 The sequence of terms together with their non-singleton runs of divisors begins:
%e A328510     1: {}
%e A328510     2: {{1,2}}
%e A328510    20: {{1,2},{4,5}}
%e A328510    90: {{1,2,3},{5,6},{9,10}}
%e A328510   630: {{1,2,3},{5,6,7},{9,10},{14,15}}
%t A328510 dv=Table[Length[DeleteCases[Length/@Split[Divisors[n],#2==#1+1&],1]],{n,1000}];
%t A328510 Table[Position[dv,i][[1,1]],{i,Union[dv]}]
%Y A328510 Equal {1} followed by the positions of first appearances in A328511 (times 2).
%Y A328510 The longest run of divisors of n has length A055874.
%Y A328510 Numbers whose divisors have no non-singleton runs are A005408.
%Y A328510 The number of successive pairs of divisors of n is A129308(n).
%Y A328510 The number of singleton runs of divisors is A132881.
%Y A328510 Cf. A000005, A027750, A033676, A060775, A119313, A132747, A181063, A199970, A328166, A328457.
%K A328510 nonn
%O A328510 0,2
%A A328510 _Gus Wiseman_, Oct 18 2019
%E A328510 Offset changed to 0 and a(10)-a(30) added by _Giovanni Resta_, Oct 25 2019