A257720 - OEIS

%I #13 Oct 31 2015 13:16:13

%S 25,34,44,74,81,106,121,124,134,184,194,202,218,268,274,284,289,314,

%T 346,361,386,394,441,514,524,529,538,554,590,604,625,634,652,674,694,

%U 698,716,724,729,752,764,778,790,794,824,841,844,884,914,922,950,974,988

%N Down-up reversals: if n is deficient and s(n) is nondeficient, where s(n) is the sum of proper divisors of n.

%C Larger member of amicable pairs (A002046) belong to this sequence.

%H Reinhard Zumkeller, <a href="/A257720/b257720.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 284 is deficient and its sum of proper divisors is 220 which in turn is nondeficient. Hence 284 is in the sequence.

%t spd[n_]:=DivisorSigma[1,n]-n;Select[Range[988],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 a257720 n = a257720_list !! (n-1)

%o a257720_list = filter f [1..] where

%o    f x = sx > 0 && 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. A257719 (up-down reversals).

%Y  Cf. A001065, A263838.

%K nonn

%O 1,1

%A _Michel Marcus_, May 05 2015