A162317 A positive integer k is included if |d(k+1) - d(k)| is a prime, where d(k) is the number of divisors of k.

5, 6, 7, 10, 13, 16, 20, 22, 24, 27, 32, 35, 36, 37, 45, 46, 48, 49, 50, 51, 58, 61, 62, 64, 68, 73, 74, 76, 80, 82, 91, 92, 99, 100, 106, 115, 117, 120, 123, 124, 143, 144, 146, 152, 153, 157, 164, 166, 168, 169, 170, 174, 178, 187, 188, 193, 196, 206, 212, 224, 225

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

24 is in the sequence because |d(25) - d(24)| = |3 - 8| = 5 is a prime. - Emeric Deutsch, Jul 12 2009

Maple

with(numtheory): a := proc (n) if isprime(abs(tau(n+1)-tau(n))) = true then n else end if end proc: seq(a(n), n = 1 .. 250); # Emeric Deutsch, Jul 12 2009

Mathematica

Flatten[Position[Partition[DivisorSigma[0, Range[250]], 2, 1], _?(PrimeQ[Abs[ First[#]-Last[#]]]&), {1}, Heads->False]] (* Harvey P. Dale, May 26 2014 *)

Crossrefs

Cf. A051950.

Sequence in context: A257604 A177089 A206415 * A162318 A350593 A108910

Adjacent sequences: A162314 A162315 A162316 * A162318 A162319 A162320

Keyword

nonn

Author

Leroy Quet, Jul 01 2009

Extensions

Extended by Emeric Deutsch, Jul 12 2009

Status

approved