A339936 Odd coreful abundant numbers: the odd terms of A308053.

99225, 165375, 231525, 297675, 496125, 694575, 826875, 893025, 1091475, 1157625, 1225125, 1289925, 1488375, 1620675, 1686825, 1819125, 1885275, 2083725, 2149875, 2282175, 2480625, 2546775, 2679075, 2811375, 2877525, 3009825, 3075975, 3142125, 3274425, 3472875

Offset

1,1

Comments

The asymptotic density of this sequence is Sum_{n>=1} f(A356871(n)) = 9.1348...*10^(-6), where f(n) = (4/(Pi^2*n))*Product_{prime p|n}(p/(p+1)) if n is odd and 0 otherwise. - Amiram Eldar, Sep 02 2022

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

99225 is a term since it is odd and the sum of its coreful divisors is A057723(99225) = 201600 > 2 * 99225.

Mathematica

f[p_, e_] := (p^(e + 1) - 1)/(p - 1) - 1; s[1] = 1; s[n_] := Times @@ (f @@@ FactorInteger[n]); Select[Range[1, 10^6, 2], s[#] > 2*# &]

Crossrefs

Intersection of A005408 and A308053.

Subsequence of A321147.

Cf. A057723, A356871.

Similar sequences: A005231, A094889, A112643, A127666, A129485, A293186, A321147, A333950.

Sequence in context: A255760 A255753 A254842 * A348275 A138732 A108224

Adjacent sequences: A339933 A339934 A339935 * A339937 A339938 A339939

Keyword

nonn

Author

Amiram Eldar, Dec 23 2020

Status

approved