A301859 Abundant numbers whose abundance is a perfect number.

48, 2002, 2632, 4540, 5170, 6952, 8925, 29056, 32445, 32980, 88330, 133042, 174856, 189472, 280228, 442365, 518368, 566752, 892552, 1266952, 2030368, 2052256, 2218450, 3959752, 4120672, 4558936, 5568448, 9071752, 15921112, 38551936, 65969536, 70114936, 88149352, 97364848

Offset

1,1

Comments

There are 34 terms up to 10^8. The abundance of odd terms (only 3 terms) is 6 (see also A087167). The abundance of even terms is 28, 496, 8128, and 33550336 (for 97364848). There exist deficient numbers whose abundance is a perfect number in absolute terms, e.g., 7, 29, 62.

Links

Amiram Eldar, Table of n, a(n) for n = 1..68

Example

48 is a term as it is abundant and its abundance, sigma(48)-2*48 = 28, is the second perfect number.

Mathematica

Select[Range[10^8], PerfectNumberQ[DivisorSigma[1, # ]-2#]&]

Prog

(PARI) for(n=1, 10^8, a=sigma(n)-2*n; a>0&&sigma(a)==2*a&&print1(n ", "))

Crossrefs

Cf. A005101 (abundant numbers), A033880 (abundance), A000396 (perfect numbers), A087167, A088834, A088012, A077374 (sequences related to the odd terms of this sequence).

Sequence in context: A276247 A274958 A165043 * A233259 A049678 A162913

Adjacent sequences: A301856 A301857 A301858 * A301860 A301861 A301862

Keyword

nonn

Author

Waldemar Puszkarz, Mar 27 2018

Status

approved