A082686 Odd nonprime integers n which have an odd number of proper divisors.

15, 21, 27, 33, 35, 39, 45, 51, 55, 57, 63, 65, 69, 75, 77, 85, 87, 91, 93, 95, 99, 105, 111, 115, 117, 119, 123, 125, 129, 133, 135, 141, 143, 145, 147, 153, 155, 159, 161, 165, 171, 175, 177, 183, 185, 187, 189, 195, 201, 203, 205, 207, 209, 213, 215, 217, 219

Offset: 1

Author

Anne Donovan (anned3005(AT)aol.com), May 19 2003

Keywords

• easy
• nonn

Comments

Odd nonprime numbers with even abundance and even sigma. Is their abundance always negative; i.e. are they always deficient? - Labos Elemer, Oct 28 2003

Odd nonprime nonsquares. - Vladeta Jovovic, Jan 25 2004

Examples

			a(1) = 15 since 15 is the first odd nonprime number with an odd number of proper divisors.
n, #proper divisors, #divisors:
9,  2, {1, 3}
15, 3, {1, 3, 5}
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Unsolved Problems (see #17). [Today this web page has only 16 sections, so this link is no longer useful. - _N. J. A. Sloane_, Nov 26 2019]

Crossrefs

Cf. A000396, A001065.

Programs

Mathematica

Select[Range[1,221,2],!PrimeQ[#]&&EvenQ[DivisorSigma[0,#]]&] (* Harvey P. Dale, Dec 16 2015 *)

PARI

isok(n) = (n % 2) && (! isprime(n)) && ((numdiv(n) % 2) == 0) \\ Michel Marcus, Jun 10 2013

Extensions

Definition corrected by Zak Seidov, Jul 21 2009