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
If the terms of this sequence are removed from A091191, then the resulting sequence will be A275082. - Timothy L. Tiffin, Jul 16 2016
REFERENCES
Guy, R. K. Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p. 46, also section B2, 1994.
LINKS
Donovan Johnson, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Primitive Abundant Number
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
Offset corrected by Donovan Johnson, Aug 28 2011
STATUS
approved