A307098 The primitive abundant numbers k (A071395) arranged by the decreasing values of their abundancy index sigma(k)/k.

3465, 15015, 4095, 1430, 19635, 16796, 20, 21945, 5355, 692835, 2584, 5985, 23205, 49742, 20332, 22309287, 26565, 188955, 1870, 216315, 838695, 25935, 3128, 22724, 6084351, 7245, 2090, 60214, 2107575, 937365, 1542773001, 25636, 28129101, 33495, 13066965, 3016174

Offset

1,1

Comments

Cohen proved that for any given eps > 0 there are only finitely many primitive abundant numbers k with sigma(k)/k >= 2 + eps. Thus the primitive abundant numbers can be arranged by their decreasing value of their abundancy index. In case of more than one primitive abundant number with the same abundancy index, the terms are ordered by their value.

Cohen calculated the first 91 terms of this sequence, all the terms with abundancy index >= 2.05 - see the link for the corresponding values of the abundancy index.

Links

Amiram Eldar, Table of n, a(n) for n = 1..91

Graeme L. Cohen, On primitive abundant numbers, Journal of the Australian Mathematical Society, Vol. 34 No. 1 (1983), pp. 123-137.

Amiram Eldar, Table of n, a(n), prime factorization of a(n), sigma(a(n))/a(n) (rounded) for n = 1..91

Example

a(1) = 3465 since it is the primitive abundant number (A071395) with the largest possible abundancy index among the primitive abundant numbers: sigma(3465)/3465 = 832/385 = 2.161003...

Crossrefs

Cf. A000203, A005100, A005101, A071395.

Sequence in context: A224686 A125017 A307111 * A251531 A251526 A325979

Adjacent sequences: A307095 A307096 A307097 * A307099 A307100 A307101

Keyword

nonn

Author

Amiram Eldar, Mar 25 2019

Status

approved