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Integers m such that d(m+1) = 2d(m) where d=A000005.
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%I #31 Feb 18 2024 08:18:49

%S 1,5,7,13,37,39,49,55,61,65,69,73,77,87,129,134,157,183,185,193,194,

%T 221,237,247,249,254,265,275,277,295,309,313,321,327,343,363,365,397,

%U 398,417,421,437,454,455,457,458,469,471,473,475,482,493,497,505,517

%N Integers m such that d(m+1) = 2d(m) where d=A000005.

%H Harry J. Smith, <a href="/A063446/b063446.txt">Table of n, a(n) for n=1..1000</a>

%e m=77, 2*d(77) = 2*4 = 8 = d(78).

%t Select[Range@ 520, DivisorSigma[0, # + 1] == 2 DivisorSigma[0, #] &] (* _Michael De Vlieger_, Feb 19 2017 *)

%o (PARI) { n=0; for (m=1, 10^9, if (numdiv(m + 1) == 2*numdiv(m), write("b063446.txt", n++, " ", m); if (n==1000, break)) ) } \\ _Harry J. Smith_, Aug 21 2009

%o (Magma) [n: n in [1..600] | NumberOfDivisors(n+1) eq (2* NumberOfDivisors(n))]; // _Vincenzo Librandi_, Aug 04 2018

%o (GAP) Filtered([1..520],n->Tau(n+1)=2*Tau(n)); # _Muniru A Asiru_, Aug 20 2018

%Y Cf. A000005.

%K nonn

%O 1,2

%A _Labos Elemer_, Jul 24 2001