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 A337381 Numbers k for which A003973(k) >= 2*sigma(k). 10
 6, 8, 9, 12, 14, 15, 16, 18, 20, 21, 24, 27, 28, 30, 32, 35, 36, 40, 42, 44, 45, 48, 49, 50, 52, 54, 56, 60, 63, 64, 66, 68, 70, 72, 75, 76, 78, 80, 81, 84, 88, 90, 92, 96, 98, 99, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Note that A003973(n) >= sigma(n) for all n. See A336852. 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 All terms are in A246282 because A341528(n) < A341529(n) for all n > 1. - Antti Karttunen, Feb 22 2021 LINKS Antti Karttunen, Table of n, a(n) for n = 1..20000 PROG (PARI) A003973(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); sigma(factorback(f)); }; isA337381(n) = (A003973(n)>=2*sigma(n)); CROSSREFS Cf. A000203, A003961, A003973, A336852, A337541, A337542, A341528, A341529. Cf. A337382 (complement), A337383 (characteristic function). Subsequences: A337378, A337384, A337386, A337543 (primitive terms). Subsequence of A246282. Sequence in context: A125736 A030725 A195101 * A305704 A043720 A191980 Adjacent sequences:  A337378 A337379 A337380 * A337382 A337383 A337384 KEYWORD nonn AUTHOR Antti Karttunen, Aug 27 2020 STATUS approved

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Last modified April 10 11:32 EDT 2021. Contains 342845 sequences. (Running on oeis4.)