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A006039 Primitive non-deficient numbers.
(Formerly M4132)
3
6, 20, 28, 70, 88, 104, 272, 304, 368, 464, 496, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A number n is non-deficient (A023196) iff it is abundant or perfect, that is iff A001065(n) is >= n. Since any multiple of a non-deficient number is itself non-deficient, we call a non-deficient number primitive iff all its proper divisors are deficient. - Jeppe Stig Nielsen, Nov 23 2003

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

T. D. Noe, Table of n, a(n) for n = 1..8671

L. E. Dickson, Finiteness of the Odd Perfect and Primitive Abundant Numbers with n Distinct Prime Factors, Amer. J. Math., 35 (1913), 413-426.

R. K. Guy, Letter to N. J. A. Sloane with attachment, Jun. 1991

FORMULA

Union of A000396 (perfect numbers) and A071395 (primitive abundant numbers). - M. F. Hasler, Jul 30 2016

MATHEMATICA

k = 1; lst = {}; While[k < 4050, If[DivisorSigma[1, k] >= 2 k && Min@Mod[k, lst] > 0, AppendTo[lst, k]]; k++]; lst (* Robert G. Wilson v, Mar 09 2017 *)

CROSSREFS

Cf. A001065 (aliquot function), A023196 (non-deficient), A005101 (abundant), A000396 (perfect), A005231 (odd abundant), A071395 (primitive abundant), A006038 (odd primitive abundant), A091191.

Sequence in context: A316291 A090502 A119425 * A180332 A064771 A006036

Adjacent sequences:  A006036 A006037 A006038 * A006040 A006041 A006042

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, R. K. Guy

STATUS

approved

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Last modified January 17 05:26 EST 2019. Contains 319207 sequences. (Running on oeis4.)