[seqfan] A294900 Interesting abundant numbers
Iain Fox
iain.fox at pacbell.net
Fri Dec 8 00:42:19 CET 2017
Dear SeqFan members,
I have been doing some investigating into the sequence, A294900, which contains all numbers such that the sum of its nonabundant divisors is itself. Naturally, this contains all perfect numbers, but I also proved that any non-perfect term is abundant. These abundant numbers would be pseudoperfect (or semiperfect) numbers. Are there any other things that these abundant terms would have in common with each other?
%I A294900
%S A294900 6,24,28,126,496,8128,5594428,33550336
%N A294900 Numbers n such that n = sum of nonabundant proper divisors of n (A294888).
%C A294900 No other terms up to 10^9. - _Michel Marcus_, Dec 01 2017
%C A294900 Naturally, all the terms of A000396, including 8589869056, are in this sequence. - _Antti Karttunen_, Dec 01 2017
%C A294900 Thus, if there are infinitely many Mersenne primes, then this sequence is also, by definition of even perfect numbers, infinite. - _Iain Fox_, Dec 02 2017
%o A294900 (PARI) isok(n) = sumdiv(n, d, if ((d<n) && (sigma(d)<=(2*d)), d)) == n; \\ _Michel Marcus_, Nov 17 2017
%Y A294900 Fixed points of A294888.
%Y A294900 Subsequence of A005835. Cf. also A000396 (a subsequence), A125310.
%K A294900 nonn,more,new
%O A294900 1,1
%A A294900 _Antti Karttunen_, Nov 14 2017
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