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

1,1

Links

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

Example

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

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 *)

Prog

(Magma) [n: n in [1..10000] | NumberOfDivisors(n) eq  NumberOfDivisors(n+3)]
(PARI) isok(n) = numdiv(n) == numdiv(n+3); \\ Michel Marcus, May 03 2017

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.

Sequence in context: A041012 A291162 A042459 * A257601 A282727 A042353

Adjacent sequences: A276710 A276711 A276712 * A276714 A276715 A276716

Keyword

nonn

Author

Jaroslav Krizek, Sep 16 2016

Status

approved