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

Author

Jean-François Alcover, May 15 2013

Keywords

• nonn
• easy
• tabf

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}.

Examples

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

Links

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

Crossrefs

Cf. A225757 (same sum of divisors).

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

Cf. A140578 (first term of every run).

Programs

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 *)