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

Author

Amiram Eldar, Dec 23 2020

Keywords

• nonn

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

Examples

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

Links

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

Crossrefs

Intersection of A005408 and A308053.

Subsequence of A321147.

Cf. A057723, A356871.

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

Programs

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*# &]