

A260577


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


3



4, 15, 16, 20, 21, 24, 27, 28, 30, 32, 33, 36, 39, 42, 45, 48, 52, 54, 55, 56, 57, 63, 64, 66, 68, 69, 75, 76, 78, 81, 85, 90, 93, 100, 105, 110, 112, 114, 116, 117, 120, 123, 126, 133, 135, 138, 140, 144, 145, 150, 153, 159, 160, 162, 165, 168, 170, 171, 172
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OFFSET

1,1


COMMENTS

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


LINKS



EXAMPLE

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


PROG

(PARI) is(n)=numdiv(n+n=numdiv(n))<n \\ M. F. Hasler, Jul 30 2015


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



