|
|
A071395
|
|
Primitive abundant numbers (abundant numbers all of whose proper divisors are deficient numbers).
|
|
48
|
|
|
20, 70, 88, 104, 272, 304, 368, 464, 550, 572, 650, 748, 836, 945, 1184, 1312, 1376, 1430, 1504, 1575, 1696, 1870, 1888, 1952, 2002, 2090, 2205, 2210, 2470, 2530, 2584, 2990, 3128, 3190, 3230, 3410, 3465, 3496, 3770, 3944, 4030, 4070, 4095, 4216, 4288
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
This is a subsequence of the primitive abundant number sequence A091191, since none of these numbers are a positive integer multiple of a perfect number (A000396). - Timothy L. Tiffin, Jul 15 2016
|
|
REFERENCES
|
Guy, R. K. Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p. 46, also section B2, 1994.
|
|
LINKS
|
|
|
EXAMPLE
|
20 is a term since 1, 2, 4, 5, and 10 (the proper divisors of 20) are all deficient numbers. - Timothy L. Tiffin, Jul 15 2016
|
|
MAPLE
|
abundance:= proc(n) option remember; numtheory:-sigma(n)-2*n end proc:
select(n -> abundance(n) > 0 and andmap(t -> abundance(t) < 0, numtheory:-divisors(n) minus {n}), [$1..10000]); # Robert Israel, Nov 15 2017
|
|
MATHEMATICA
|
Select[Range@ 5000, DivisorSigma[1, #] > 2 # && Times @@ Boole@ Map[DivisorSigma[1, #] < 2 # &, Most@ Divisors@ #] == 1 &] (* Michael De Vlieger, Jul 16 2016 *)
|
|
PROG
|
(PARI) isA071395(v) = {if (sigma(v) <= 2*v, return (0)); fordiv (v, d, if ((d != v) && (sigma(d) >= 2*d), return (0)); ); return (1); } \\ Michel Marcus, Mar 10 2013
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Joe McCauley (mccauley(AT)davesworld.net), Jun 12 2002
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|