A260577 Numbers n for which d(n+d(n)) < d(n), where d(n) is the number of divisors of n.

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

Offset: 1

Author

Vladimir Shevelev, Jul 29 2015

Keywords

• nonn

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

Examples

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

Links

• Peter J. C. Moses, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A000005, A175304.

Programs

PARI

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