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A349759 Nobly deficient numbers: numbers k such that both d(k) = A000005(k) and sigma(k) = A000203(k) are deficient numbers (A005100).

%I A349759 #15 Dec 06 2021 03:12:43
%S A349759 1,2,3,4,7,8,9,13,16,21,25,31,36,37,43,48,49,61,64,67,73,81,93,97,100,
%T A349759 109,111,112,121,127,128,144,151,157,162,163,169,181,183,192,193,196,
%U A349759 208,211,217,219,225,229,241,256,277,283,289,313,324,331,337,361,373
%N A349759 Nobly deficient numbers: numbers k such that both d(k) = A000005(k) and sigma(k) = A000203(k) are deficient numbers (A005100).
%C A349759 Analogous to sublime numbers (A081357), with deficient numbers instead of perfect numbers.
%C A349759 If p != 5 is a prime such that (p+1)/2 is also a prime (i.e., p is in A005383 \ {5}), then p is a term of this sequence.
%H A349759 Amiram Eldar, <a href="/A349759/b349759.txt">Table of n, a(n) for n = 1..10000</a>
%H A349759 Jason Earls, <a href="https://dl.acm.org/doi/abs/10.5555/1006498.1006546">Some Smarandache-type sequences and problems concerning abundant and deficient numbers</a>, Smarandache Notions Journal, Vol. 14, No. 1 (2004), pp. 243-250.
%H A349759 József Sándor, <a href="https://blngcc.files.wordpress.com/2008/11/jozsel-sandor-selected-chaters-of-geometry-analysis-and-number-theory.pdf">Selected Chapters of Geometry, Analysis and Number Theory</a>, 2005, pp. 132-134.
%H A349759 Shikha Yadav and Surendra Yadav, <a href="http://raops.org.in/epapers/dec16_10.pdf">Multiplicatively perfect and related numbers</a>, Journal of Rajasthan Academy of Physical Sciences, Vol. 15, No. 4 (2016), pp. 345-350.
%e A349759 2 is a term since both d(2) = 2 and sigma(2) = 3 are deficient numbers.
%t A349759 defQ[n_] := DivisorSigma[1, n] < 2*n; nobDefQ[n_] := And @@ defQ /@ DivisorSigma[{0, 1}, n]; Select[Range[400], nobDefQ]
%o A349759 (PARI) isdef(k) = sigma(k) < 2*k; \\ A005100
%o A349759 isok(k) = my(f=factor(k)); isdef(numdiv(f)) && isdef(sigma(f)); \\ _Michel Marcus_, Dec 03 2021
%Y A349759 Cf. A000005, A000203, A005100, A005383, A081357, A349758.
%K A349759 nonn
%O A349759 1,2
%A A349759 _Amiram Eldar_, Nov 29 2021