cp's OEIS Frontend

A328511 Number of non-singleton runs of divisors of 2n.

%I A328511 #15 Oct 25 2019 11:14:19
%S A328511 1,1,1,1,1,1,1,1,1,2,1,1,1,1,2,1,1,1,1,2,2,1,1,1,1,1,1,2,1,1,1,1,1,1,
%T A328511 1,2,1,1,1,2,1,2,1,1,3,1,1,1,1,2,1,1,1,1,2,2,1,1,1,1,1,1,2,1,1,2,1,1,
%U A328511 1,2,1,2,1,1,2,1,1,2,1,2,1,1,1,2,1,1,1
%N A328511 Number of non-singleton runs of divisors of 2n.
%H A328511 Robert Israel, <a href="/A328511/b328511.txt">Table of n, a(n) for n = 1..10000</a>
%H A328511 Wikipedia, <a href="https://en.wikipedia.org/wiki/Run_(cards)">Run (cards)</a>
%e A328511 The divisors of 90 have runs: {{1, 2, 3}, {5, 6}, {9, 10}, {15}, {18}, {30}, {45}, {90}}, so a(45) = 3.
%p A328511 f:= proc(n) local D,B,R;
%p A328511   D:= sort(convert(numtheory:-divisors(2*n),list));
%p A328511   B:= D[2..-1]-D[1..-2];
%p A328511   R:= select(j -> (j=1 or B[j-1]>1) and B[j]=1, [$1..nops(B)]);
%p A328511   nops(R);
%p A328511 end proc:
%p A328511 map(f, [$1..100]); # _Robert Israel_, Oct 25 2019
%t A328511 Table[Length[DeleteCases[Length/@Split[Divisors[2*n],#2==#1+1&],1]],{n,100}]
%Y A328511 Positions of first appearances are A328510.
%Y A328511 The longest run of divisors of n has length A055874.
%Y A328511 Numbers whose divisors have no non-singleton runs are A005408.
%Y A328511 The number of successive pairs of divisors of n is A129308(n).
%Y A328511 The number of singleton runs of divisors is A132881.
%Y A328511 Cf. A000005, A033676, A060775, A119313, A132747, A181063, A199970, A328166, A328457.
%K A328511 nonn
%O A328511 1,10
%A A328511 _Gus Wiseman_, Oct 18 2019