

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
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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
Index entries for sequences computed from indices in prime factorization
Index entries for sequences related to sigma(n)


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



