

A082686


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


3



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
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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



