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A071395 Primitive abundant numbers (abundant numbers all of whose proper divisors are deficient numbers). 9
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

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

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 * A245856 A053741 A052516

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 December 4 21:33 EST 2016. Contains 278755 sequences.