A276713 - OEIS

%I #13 Nov 12 2022 13:12:02

%S 2,35,55,62,74,82,91,102,115,119,122,135,142,143,155,158,172,186,202,

%T 203,206,214,215,218,242,255,259,262,282,295,298,299,302,323,326,343,

%U 351,354,355,362,391,395,399,425,426,435,451,466,478,482,492,502,511,514

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

%H Jaroslav Krizek, <a href="/A276713/b276713.txt">Table of n, a(n) for n = 1..1000</a>

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

%p 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

%t SequencePosition[DivisorSigma[0,Range[600]],{x_,_,_,x_}][[All,1]] (* _Harvey P. Dale_, Nov 12 2022 *)

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

%o (PARI) isok(n) = numdiv(n) == numdiv(n+3); \\ _Michel Marcus_, May 03 2017

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

%Y 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.

%K nonn

%O 1,1

%A _Jaroslav Krizek_, Sep 16 2016