A162318 A positive integer n is included if |d(n+1)-d(n)| = 2, where d(n) is the number of divisors of n.

5, 6, 7, 10, 13, 20, 22, 27, 32, 37, 45, 46, 50, 51, 58, 61, 62, 68, 73, 74, 76, 82, 91, 92, 106, 115, 117, 123, 124, 146, 152, 153, 157, 164, 166, 170, 174, 178, 187, 188, 193, 206, 212, 226, 235, 236, 245, 261, 262, 267, 272, 274, 277, 278, 284, 291, 313, 325

Offset

1,1

Links

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

Example

68 is included because |d(69)-d(68)| = |4 - 6| = 2. [Emeric Deutsch, Jul 12 2009]

Maple

with(numtheory): a := proc (n) if abs(tau(n+1)-tau(n)) = 2 then n else end if end proc; seq(a(n), n = 1 .. 350); # Emeric Deutsch, Jul 12 2009

Mathematica

Select[Range[500], Abs[DivisorSigma[0, # + 1] - DivisorSigma[0, #]] == 2 &] (* Indranil Ghosh, Mar 26 2017 *)
Position[Abs[Differences[DivisorSigma[0, Range[350]]]], 2]//Flatten (* Harvey P. Dale, Aug 14 2017 *)

Prog

(PARI) isok(n) = abs(numdiv(n+1) - numdiv(n)) == 2; \\ Michel Marcus, Mar 26 2017
(Python)
from sympy import divisor_count
print([n for n in range(500) if abs(divisor_count(n + 1) - divisor_count(n)) == 2]) # Indranil Ghosh, Mar 26 2017

Crossrefs

Sequence in context: A177089 A206415 A162317 * A350593 A108910 A308193

Adjacent sequences: A162315 A162316 A162317 * A162319 A162320 A162321

Keyword

nonn

Author

Leroy Quet, Jul 01 2009

Extensions

Extended by Emeric Deutsch, Jul 12 2009

Status

approved