

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
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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



