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

Author

Leroy Quet, Jul 01 2009

Keywords

• nonn

Examples

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

Links

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

Programs

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 *)

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

Extensions

Extended by Emeric Deutsch, Jul 12 2009