A257719 Up-down reversals: nondeficient n with deficient sum of proper divisors of n.

12, 18, 20, 36, 40, 48, 56, 70, 72, 80, 88, 100, 104, 108, 112, 144, 156, 160, 162, 192, 196, 200, 208, 220, 228, 260, 272, 288, 300, 304, 320, 324, 336, 350, 352, 368, 372, 392, 400, 416, 432, 448, 450, 460, 464, 468, 490, 500, 516, 544, 550, 572, 576, 608

Offset

1,1

Comments

Lesser member of amicable pairs (A002025) belong to this sequence.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

P. Pollack and C. Pomerance, Some problems of Erdos on the sum-of-divisors function, 2015.

Example

220 is abundant (nondeficient) and its sum of proper divisors is 284 which in turn is deficient. Hence 220 is in the sequence.

Mathematica

spd[n_]:=DivisorSigma[1, n]-n; Select[Range[608], spd[#]>=#&&spd[spd[#]]<spd[#]&] (* Ivan N. Ianakiev, May 06 2015 *)

Prog

(PARI) isok(n) = (sn = sigma(n)-n) && (sn >= n) && (sigma(sn) < 2*sn);
(Haskell)
a257719 n = a257719_list !! (n-1)
a257719_list = filter f [1..] where
   f x = sx >= x && a001065 sx < sx where sx = a001065 x
-- Reinhard Zumkeller, Oct 31 2015

Crossrefs

Cf. A000396 (perfect), A005100 (deficient), A005101 (abundant).

Cf. A000203 (sum of divisors), A001065 (sum of proper divisors).

Cf. A257720 (down-up reversals).

Cf. A001065, A263838.

Sequence in context: A091191 A357696 A259980 * A071927 A362052 A247625

Adjacent sequences: A257716 A257717 A257718 * A257720 A257721 A257722

Keyword

nonn

Author

Michel Marcus, May 05 2015

Status

approved