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

1,1

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

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]

Example

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}

Mathematica

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

Prog

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

Crossrefs

Cf. A000396, A001065.

Sequence in context: A134642 A072974 A226025 * A102030 A168104 A026048

Adjacent sequences: A082683 A082684 A082685 * A082687 A082688 A082689

Keyword

easy,nonn

Author

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

Extensions

Definition corrected by Zak Seidov, Jul 21 2009

Status

approved