A158338 Composite numbers k such that k - number of divisors of k = prime.

6, 15, 16, 21, 27, 33, 35, 51, 57, 65, 77, 87, 93, 105, 111, 135, 141, 143, 155, 161, 165, 177, 183, 185, 189, 201, 203, 215, 231, 237, 245, 267, 275, 285, 287, 321, 335, 341, 345, 357, 371, 375, 377, 393, 413, 425, 429, 437, 447, 453, 465, 471

Offset: 1

Author

Juri-Stepan Gerasimov, Mar 16 2009, Nov 14 2009

Keywords

• nonn

Comments

Subsequence of A067531. - Michel Marcus, Dec 22 2014

Examples

			6 is composite and has 4 divisors (1, 2, 3, 6); 6 - 4 = 2, which is prime, so 6 is in the sequence.
15 is composite and has 4 divisors (1, 3, 5, 15); 15 - 4 = 11, which is prime, so 15 is in the sequence.
16 is composite and has 5 divisors (1, 2, 4, 8, 16); 16 - 5 = 11, which is prime, so 16 is in the sequence.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A000040, A002808, A035004, A067531.

Programs

Magma

[k:k in [1..500]|not IsPrime(k) and IsPrime(k-#Divisors(k))]; // Marius A. Burtea, Jul 16 2019

Mathematica

Select[Range[500], CompositeQ[#] && PrimeQ[# - DivisorSigma[0, #]] &] (* Amiram Eldar, Jul 16 2019 *)

Extensions

Extended by R. J. Mathar, May 19 2010