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A344586 Numbers k for which A003415(k) >= A001065(k), where A003415 gives the arithmetic derivative, and A001065 is the sum of proper divisors.

%I A344586 #12 Jun 08 2021 06:27:16
%S A344586 1,2,3,4,5,7,8,9,11,12,13,16,17,18,19,20,23,24,25,27,28,29,31,32,36,
%T A344586 37,40,41,43,44,45,47,48,49,50,52,53,54,56,59,61,63,64,67,68,71,72,73,
%U A344586 75,76,79,80,81,83,88,89,92,96,97,98,99,100,101,103,104,107,108,109,112,113,116,117,120,121,124,125,127,128,131
%N A344586 Numbers k for which A003415(k) >= A001065(k), where A003415 gives the arithmetic derivative, and A001065 is the sum of proper divisors.
%H A344586 Antti Karttunen, <a href="/A344586/b344586.txt">Table of n, a(n) for n = 1..20000</a>
%o A344586 (PARI)
%o A344586 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A344586 isA344586(n) = (A003415(n) >= (sigma(n)-n));
%Y A344586 Cf. A001065, A003415.
%Y A344586 Cf. A212127, A212128 (subsequences), A344585 (complement).
%Y A344586 Positions of nonnegative terms in A211991.
%Y A344586 Differs from A212165 for the first time at n=121, where a(121) = 220, while A212165(121) = 223.
%K A344586 nonn
%O A344586 1,2
%A A344586 _Antti Karttunen_, May 24 2021