A260577 - OEIS

%I #14 Aug 01 2015 17:02:22

%S 4,15,16,20,21,24,27,28,30,32,33,36,39,42,45,48,52,54,55,56,57,63,64,

%T 66,68,69,75,76,78,81,85,90,93,100,105,110,112,114,116,117,120,123,

%U 126,133,135,138,140,144,145,150,153,159,160,162,165,168,170,171,172

%N Numbers n for which d(n+d(n)) < d(n), where d(n) is the number of divisors of n.

%C All terms are composite.

%C Indeed, if p is prime then d(p)=2 will never be larger than d(p+d(p)) = d(p+2). - _M. F. Hasler_, Jul 30 2015

%C Conjecture: for every x>=6, among the first x terms, the terms divisible by 3 are never in the minority.

%C Let A(y) be the number of terms <= y, y>=1. If the conjecture is true, then, taking into account the initials, we conclude that always A(y) < (2/3)*y. - _Vladimir Shevelev_, Jul 31 2015

%H Peter J. C. Moses, <a href="/A260577/b260577.txt">Table of n, a(n) for n = 1..2000</a>

%e 75 is in the sequence, since d(75) = 6 > d(75+6) = 5.

%o (PARI) is(n)=numdiv(n+n=numdiv(n))<n \\ _M. F. Hasler_, Jul 30 2015

%Y Cf. A000005, A175304.

%K nonn

%O 1,1

%A _Vladimir Shevelev_, Jul 29 2015