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A337381 Numbers k for which A003973(k) >= 2*sigma(k).

%I A337381 #23 Feb 28 2021 20:28:06
%S A337381 6,8,9,12,14,15,16,18,20,21,24,27,28,30,32,35,36,40,42,44,45,48,49,50,
%T A337381 52,54,56,60,63,64,66,68,70,72,75,76,78,80,81,84,88,90,92,96,98,99,
%U A337381 100,102,104,105,108,110,112,114,117,120,124,125,126,128,130,132,135,136,138,140,144,147,148,150,152,153,154
%N A337381 Numbers k for which A003973(k) >= 2*sigma(k).
%C A337381 Note that A003973(n) >= sigma(n) for all n. See A336852.
%C A337381 Like the abundancy index (ratio A000203(n)/n), and ratio A003961(n)/n, the ratio A003973(n)/sigma(n) is also multiplicative and > 1 for all n > 1. Thus if the number has a proper divisor that is in this sequence, then the number itself is also. See A337543 for those terms included here, but which have no proper divisor in this sequence. - _Antti Karttunen_, Aug 31 2020
%C A337381 All terms are in A246282 because A341528(n) < A341529(n) for all n > 1. - _Antti Karttunen_, Feb 22 2021
%H A337381 Antti Karttunen, <a href="/A337381/b337381.txt">Table of n, a(n) for n = 1..20000</a>
%H A337381 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A337381 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%o A337381 (PARI)
%o A337381 A003973(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); sigma(factorback(f)); };
%o A337381 isA337381(n) = (A003973(n)>=2*sigma(n));
%Y A337381 Cf. A000203, A003961, A003973, A336852, A337541, A337542, A341528, A341529.
%Y A337381 Cf. A337382 (complement), A337383 (characteristic function).
%Y A337381 Subsequences: A337378, A337384, A337386, A337543 (primitive terms).
%Y A337381 Subsequence of A246282.
%K A337381 nonn
%O A337381 1,1
%A A337381 _Antti Karttunen_, Aug 27 2020