A328510 -id:A328510 - cp's OEIS frontend

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

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, 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, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1

Offset: 1

Gus Wiseman, Oct 18 2019

nonn

			The divisors of 90 have runs: {{1, 2, 3}, {5, 6}, {9, 10}, {15}, {18}, {30}, {45}, {90}}, so a(45) = 3.

Robert Israel, Table of n, a(n) for n = 1..10000
Wikipedia, Run (cards)

Positions of first appearances are A328510.
The longest run of divisors of n has length A055874.
Numbers whose divisors have no non-singleton runs are A005408.
The number of successive pairs of divisors of n is A129308(n).
The number of singleton runs of divisors is A132881.
Cf. A000005, A033676, A060775, A119313, A132747, A181063, A199970, A328166, A328457.

f:= proc(n) local D,B,R;
  D:= sort(convert(numtheory:-divisors(2*n),list));
  B:= D[2..-1]-D[1..-2];
  R:= select(j -> (j=1 or B[j-1]>1) and B[j]=1, [$1..nops(B)]);
  nops(R);
end proc:
map(f, [$1..100]); # Robert Israel, Oct 25 2019

Table[Length[DeleteCases[Length/@Split[Divisors[2*n],#2==#1+1&],1]],{n,100}]

cp's OEIS Frontend

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

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