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A301859 Abundant numbers whose abundance is a perfect number. 1
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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..34.

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

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Last modified April 24 18:03 EDT 2019. Contains 322430 sequences. (Running on oeis4.)