A276713 Numbers n such that n and n+3 have the same number of divisors (A000005).

2, 35, 55, 62, 74, 82, 91, 102, 115, 119, 122, 135, 142, 143, 155, 158, 172, 186, 202, 203, 206, 214, 215, 218, 242, 255, 259, 262, 282, 295, 298, 299, 302, 323, 326, 343, 351, 354, 355, 362, 391, 395, 399, 425, 426, 435, 451, 466, 478, 482, 492, 502, 511, 514

Offset: 1

Author

Jaroslav Krizek, Sep 16 2016

Keywords

• nonn

Examples

			35 is in sequence because tau(35) = tau(38) = 4.
		

Links

• Jaroslav Krizek, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A065559 (smallest k such that tau(k) = tau(k+n)), A015861 (sigma(n) = sigma(n+3)), A276714.

Cf. Similar sequences with numbers n such that n and n+k have the same number of divisors for k = 1: A005237, for k = 2: A062832.

Programs

Magma

[n: n in [1..10000] | NumberOfDivisors(n) eq  NumberOfDivisors(n+3)]

Maple

with(numtheory): A276713:=n->`if`(tau(n) = tau(n+3), n, NULL): seq(A276713(n), n=1..10^3); # Wesley Ivan Hurt, May 02 2017

Mathematica

SequencePosition[DivisorSigma[0,Range[600]],{x_,,,x_}][[All,1]] (* Harvey P. Dale, Nov 12 2022 *)

PARI

isok(n) = numdiv(n) == numdiv(n+3); \\ Michel Marcus, May 03 2017