A068208 Numbers n such that tau(n) - tau(n+1) = 1.

4, 8, 81, 441, 625, 1089, 2024, 2401, 3025, 3968, 5624, 5929, 6561, 6723, 7569, 8281, 8463, 12321, 13225, 13688, 14161, 14641, 14884, 15375, 16641, 20164, 21608, 24025, 25921, 26895, 28561, 34225, 46225, 55225, 55695, 61009, 62001, 67081

Offset

1,1

Comments

a(n) cannot be a prime.

a(n) or a(n) + 1 is a perfect square as its number of divisors must be odd. - David A. Corneth, Dec 26 2020

Links

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1000 terms from Enrique Pérez Herrero)

Formula

n such that A000005(n) - A000005(n+1) = 1.

Mathematica

Select[Range[10^5], DivisorSigma[0, #] - DivisorSigma[0, # + 1] == 1 &] (* Michael De Vlieger, Dec 02 2015 *)
Position[Differences[DivisorSigma[0, Range[70000]]], -1]//Flatten (* Harvey P. Dale, May 22 2020 *)

Prog

(PARI) isok(n) = numdiv(n) - numdiv(n+1) == 1; \\ Michel Marcus, Dec 02 2015

Crossrefs

Cf. A000005.

Sequence in context: A236284 A276979 A221256 * A090254 A222287 A120281

Adjacent sequences: A068205 A068206 A068207 * A068209 A068210 A068211

Keyword

nonn,easy

Author

Benoit Cloitre, Mar 23 2002

Status

approved