

A060326


Numbers n such that 2*n  sigma(n) is a divisor of n and greater than one, where sigma = A000203 is the sum of divisors.


2



10, 44, 136, 152, 184, 752, 884, 2144, 2272, 2528, 8384, 12224, 17176, 18632, 18904, 32896, 33664, 34688, 49024, 63248, 85936, 106928, 116624, 117808, 526688, 527872, 531968, 556544, 589312, 599072, 654848, 709784, 801376, 879136, 885928, 1090912
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

For n=2^k, sigma(n)=2n1, so that 2nsigma(n)=1 would trivially divide n. These n are excluded. All abundant numbers (with sigma(n)>2n) are also excluded, even when sigma(n)2n divides n, as for n=12 which is a multiple of 2nsigma(n) = 4.  M. F. Hasler, Jul 21 2012
The sequence can also be obtained by looking for numbers whose abundancy sigma(n)/n with form (2*k1)/k (hence deficient), while excluding powers of 2.  Michel Marcus, Oct 07 2013


LINKS

R. J. Mathar and Donovan Johnson, Table of n, a(n) for n = 1..200 (first 42 terms from R. J. Mathar)


FORMULA

{ m in A005100 \ A000079 : A033879(m) divides m }.  M. F. Hasler, Jul 21 2012


EXAMPLE

10 is a member because the divisors of 10 are 1,2,5,10, with sum 18 and 2*n18 = 2, which divides 10. Or sigma(10)/10 = 9/5 = (2*k1)/k with k=5.


MATHEMATICA

sdnQ[n_]:=Module[{c=2nDivisorSigma[1, n]}, c>1&&Divisible[n, c]]; Select[ Range[600000], sdnQ] (* Harvey P. Dale, Jul 23 2012 *)


PROG

(PARI) for(n=1, 6e5, (t=2*nsigma(n))>1 & !(n%t) & print1(n", ")) \\  M. F. Hasler, Jul 21 2012


CROSSREFS

Cf. A214408.
Sequence in context: A085582 A058310 A005720 * A200448 A124852 A220923
Adjacent sequences: A060323 A060324 A060325 * A060327 A060328 A060329


KEYWORD

nonn


AUTHOR

Phil Mason (hattrack(AT)usa.net)


EXTENSIONS

More terms from Michel Marcus, Oct 07 2013


STATUS

approved



