A257720 Down-up reversals: if n is deficient and s(n) is nondeficient, where s(n) is the sum of proper divisors of n.

25, 34, 44, 74, 81, 106, 121, 124, 134, 184, 194, 202, 218, 268, 274, 284, 289, 314, 346, 361, 386, 394, 441, 514, 524, 529, 538, 554, 590, 604, 625, 634, 652, 674, 694, 698, 716, 724, 729, 752, 764, 778, 790, 794, 824, 841, 844, 884, 914, 922, 950, 974, 988

Offset

1,1

Comments

Larger member of amicable pairs (A002046) 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

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

Mathematica

spd[n_]:=DivisorSigma[1, n]-n; Select[Range[988], 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)
a257720 n = a257720_list !! (n-1)
a257720_list = filter f [1..] where
   f x = sx > 0 && 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. A257719 (up-down reversals).

Cf. A001065, A263838.

Sequence in context: A227516 A281369 A188059 * A098368 A281370 A101066

Adjacent sequences: A257717 A257718 A257719 * A257721 A257722 A257723

Keyword

nonn

Author

Michel Marcus, May 05 2015

Status

approved