A067290 Numbers n such that prime(n)<n*tau(n) where tau(n) is the number of divisors of n.

2, 3, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 26, 27, 28, 30, 32, 36, 40, 42, 44, 45, 48, 50, 52, 54, 56, 60, 63, 64, 66, 68, 70, 72, 75, 76, 78, 80, 84, 88, 90, 92, 96, 98, 99, 100, 102, 104, 105, 108, 110, 112, 114, 116, 117, 120, 124, 126, 128, 130, 132

Offset

1,1

Comments

Visible sharp bends on the graph around the 500th and 15000th terms occur where the ratio prime(n)/n exceeds 8 and 12, correspondingly. - Ivan Neretin, Oct 16 2016

Links

Ivan Neretin, Table of n, a(n) for n = 1..20000

Mathematica

Select[Range@135, Prime[#] < #*DivisorSigma[0, #] &] (* Ivan Neretin, Oct 16 2016 *)

Prog

(PARI) for(n=1, 171, if(prime(n)<n*numdiv(n), print1(n, ", ")))

Crossrefs

Cf. A000005.

Sequence in context: A353684 A047229 A094229 * A106577 A068577 A225731

Adjacent sequences: A067287 A067288 A067289 * A067291 A067292 A067293

Keyword

nonn

Author

Benoit Cloitre, Feb 24 2002

Status

approved