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%I #12 Oct 31 2015 13:15:45
%S 12,18,20,36,40,48,56,70,72,80,88,100,104,108,112,144,156,160,162,192,
%T 196,200,208,220,228,260,272,288,300,304,320,324,336,350,352,368,372,
%U 392,400,416,432,448,450,460,464,468,490,500,516,544,550,572,576,608
%N Up-down reversals: nondeficient n with deficient sum of proper divisors of n.
%C Lesser member of amicable pairs (A002025) belong to this sequence.
%H Reinhard Zumkeller, <a href="/A257719/b257719.txt">Table of n, a(n) for n = 1..10000</a>
%H P. Pollack and C. Pomerance, <a href="https://math.dartmouth.edu/~carlp/reversal12.pdf">Some problems of Erdos on the sum-of-divisors function</a>, 2015.
%e 220 is abundant (nondeficient) and its sum of proper divisors is 284 which in turn is deficient. Hence 220 is in the sequence.
%t spd[n_]:=DivisorSigma[1,n]-n;Select[Range[608],spd[#]>=#&&spd[spd[#]]<spd[#]&] (* _Ivan N. Ianakiev_, May 06 2015 *)
%o (PARI) isok(n) = (sn = sigma(n)-n) && (sn >= n) && (sigma(sn) < 2*sn);
%o (Haskell)
%o a257719 n = a257719_list !! (n-1)
%o a257719_list = filter f [1..] where
%o f x = sx >= x && a001065 sx < sx where sx = a001065 x
%o -- _Reinhard Zumkeller_, Oct 31 2015
%Y Cf. A000396 (perfect), A005100 (deficient), A005101 (abundant).
%Y Cf. A000203 (sum of divisors), A001065 (sum of proper divisors).
%Y Cf. A257720 (down-up reversals).
%Y Cf. A001065, A263838.
%K nonn
%O 1,1
%A _Michel Marcus_, May 05 2015
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