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

1,10

Links

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

Wikipedia, Run (cards)

Example

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

Maple

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

Mathematica

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

Crossrefs

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.

Sequence in context: A032542 A107038 A236833 * A371245 A043278 A125238

Adjacent sequences: A328508 A328509 A328510 * A328512 A328513 A328514

Keyword

nonn

Author

Gus Wiseman, Oct 18 2019

Status

approved