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A071395
Primitive abundant numbers (abundant numbers all of whose proper divisors are deficient numbers).
50
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
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
Numbers n such that A294927(n) = 0 and A294937(n) = 1. - Antti Karttunen, Nov 14 2017
REFERENCES
Guy, R. K. Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p. 46, also section B2, 1994.
LINKS
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
Cf. A006038, A000396, A005100, A005101, subsequence of A091191, A275082.
Sequence in context: A238101 A153728 A234367 * A362053 A357921 A335557
KEYWORD
nonn
AUTHOR
Joe McCauley (mccauley(AT)davesworld.net), Jun 12 2002
EXTENSIONS
Offset corrected by Donovan Johnson, Aug 28 2011
STATUS
approved