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

1,1

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

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

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

Cf. A000005, A175304.

Sequence in context: A229412 A076349 A175959 * A152442 A161769 A135658

Adjacent sequences: A260574 A260575 A260576 * A260578 A260579 A260580

Keyword

nonn

Author

Vladimir Shevelev, Jul 29 2015

Status

approved