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%I M4132 #54 Nov 29 2022 12:53:15
%S 6,20,28,70,88,104,272,304,368,464,496,550,572,650,748,836,945,1184,
%T 1312,1376,1430,1504,1575,1696,1870,1888,1952,2002,2090,2205,2210,
%U 2470,2530,2584,2990,3128,3190,3230,3410,3465,3496,3770,3944,4030
%N Primitive non-deficient numbers.
%C 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
%C Numbers whose proper multiples are all abundant, and whose proper divisors are all deficient. - _Peter Munn_, Sep 08 2020
%C As a set, shares with the sets of k-almost primes this property: no member divides another member and each positive integer not in the set is either a divisor of 1 or more members of the set or a multiple of 1 or more members of the set, but not both. See A337814 for proof etc. - _Peter Munn_, Apr 13 2022
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H T. D. Noe, <a href="/A006039/b006039.txt">Table of n, a(n) for n = 1..8671</a>
%H L. E. Dickson, <a href="http://www.jstor.org/stable/2370405">Finiteness of the Odd Perfect and Primitive Abundant Numbers with n Distinct Prime Factors</a>, Amer. J. Math., 35 (1913), 413-426.
%H R. K. Guy, <a href="/A001599/a001599_1.pdf">Letter to N. J. A. Sloane with attachment, Jun. 1991</a>
%H Jared Duker Lichtman, <a href="https://doi.org/10.1016/j.jnt.2018.03.021">The reciprocal sum of primitive nondeficient numbers</a>, Journal of Number Theory, Vol. 191 (2018), pp. 104-118.
%H <a href="/index/O#opnseqs">Index entries for sequences where any odd perfect numbers must occur</a>
%F Union of A000396 (perfect numbers) and A071395 (primitive abundant numbers). - _M. F. Hasler_, Jul 30 2016
%F Sum_{n>=1} 1/a(n) is in the interval (0.34842, 0.37937) (Lichtman, 2018). - _Amiram Eldar_, Jul 15 2020
%t 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 *)
%Y Cf. A001065 (aliquot function), A023196 (non-deficient), A005101 (abundant), A091191.
%Y Subsequences: A000396 (perfect), A071395 (primitive abundant), A006038 (odd primitive abundant), A333967, A352739.
%Y Positions of 1's in A341620 and in A337690.
%Y Cf. A180332, A337479, A337688, A337689, A337691, A337814, A338133 (sorted by largest prime factor), A338427 (largest prime(n)-smooth), A341619 (characteristic function), A342669.
%K nonn
%O 1,1
%A _N. J. A. Sloane_, _R. K. Guy_
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