A225756 Runs of consecutive numbers with the same number of divisors.

2, 3, 14, 15, 21, 22, 26, 27, 33, 34, 35, 38, 39, 44, 45, 57, 58, 75, 76, 85, 86, 87, 93, 94, 95, 98, 99, 104, 105, 116, 117, 118, 119, 122, 123, 133, 134, 135, 136, 141, 142, 143, 145, 146, 147, 148, 158, 159, 171, 172, 177, 178, 189, 190, 201, 202, 203

Offset

1,1

Comments

The first run of length 3 is {33,34,35}; the first of length 4: {116, 117, 118, 119}; of length 5: {2641, 2642, 2643, 2644, 2645}; of length 6: {1081, 1082, 1083, 1084, 1085, 1086}; of length 7: {25781, 25782, 25783, 25784, 25785, 25786, 25787}; of length 8: {77673, 77674, 77675, 77676, 77677, 77678, 77679, 77680}.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Example

Sequence begins:
2, 3;
14, 15;
21, 22;
26, 27;
33, 34, 35;
38, 39;
etc.

Mathematica

sel = Select[Range[300], DivisorSigma[0, #] == DivisorSigma[0, # + 1] &]; Union[sel, sel + 1]
Flatten[SequencePosition[DivisorSigma[0, Range[300]], {x_, x_}]]//Union (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 22 2021 *)

Crossrefs

Cf. A225757 (same sum of divisors).

Cf. A225758 (same number and sum of divisors).

Cf. A140578 (first term of every run).

Sequence in context: A244295 A032806 A353870 * A260143 A353871 A275303

Adjacent sequences: A225753 A225754 A225755 * A225757 A225758 A225759

Keyword

nonn,easy,tabf

Author

Jean-François Alcover, May 15 2013

Status

approved