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 A071395 Primitive abundant numbers (abundant numbers all of whose proper divisors are deficient numbers). 49
 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 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 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 Cf. A006038, A000396, A005100, A005101, subsequence of A091191, A275082. Cf. A294927, A294937. Sequence in context: A238101 A153728 A234367 * A362053 A357921 A335557 Adjacent sequences: A071392 A071393 A071394 * A071396 A071397 A071398 KEYWORD nonn AUTHOR Joe McCauley (mccauley(AT)davesworld.net), Jun 12 2002 EXTENSIONS Offset corrected by Donovan Johnson, Aug 28 2011 STATUS approved

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Last modified August 8 01:04 EDT 2024. Contains 375018 sequences. (Running on oeis4.)