A354282 Weird numbers k such that k+1 is the sum of a subset of the aliquot divisors of k.

70, 836, 4030, 5830, 7192, 7912, 10792, 17272, 45356, 83312, 91388, 113072, 222952, 243892, 254012, 388076, 410476, 786208, 1713592, 4145216, 4199030, 4632896, 6911512, 7257530, 7354304, 7607530, 9928792, 10402490, 10580624, 11339816, 11547352, 12052390, 13086016

Offset

1,1

Comments

First differs from A258250 and A329190 at n=13.

There are 17270452 weird numbers below 10^10 and only 94 are in this sequence.

Links

Amiram Eldar, Table of n, a(n) for n = 1..94

Example

70 is a term since it is a weird number, its aliquot divisors are {1, 2, 5, 7, 10, 14, 35} and 71 = 5 + 7 + 10 + 14 + 35.

Mathematica

q[n_] := Module[{d = Most @ Divisors[n], x, s, c}, If[Plus @@ d <= n, False, s = Series[Product[1 + x^d[[i]], {i, Length[d]}], {x, 0, n + 1}]; c = SeriesCoefficient[s, #] & /@ (n + {0, 1}); c[[1]] == 0 && c[[2]] > 0]]; Select[Range[10000], q]

Prog

(PARI) is(n, d=divisors(n)[^-1], s=vecsum(d))={s>n && !is_A005835(n, d, s) && is_A005835(n+1, d, s)}; \\ using is_A005835() by M. F. Hasler at A005835

Crossrefs

Subsequence of A006037.

A354283 is a subsequence.

Cf. A005835, A258250, A329190, A354281.

Sequence in context: A364862 A006037 A002975 * A329190 A258250 A349285

Adjacent sequences: A354279 A354280 A354281 * A354283 A354284 A354285

Keyword

nonn

Author

Amiram Eldar, May 22 2022

Status

approved