A354282 - OEIS

%I #8 May 24 2022 06:14:35

%S 70,836,4030,5830,7192,7912,10792,17272,45356,83312,91388,113072,

%T 222952,243892,254012,388076,410476,786208,1713592,4145216,4199030,

%U 4632896,6911512,7257530,7354304,7607530,9928792,10402490,10580624,11339816,11547352,12052390,13086016

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

%C First differs from A258250 and A329190 at n=13.

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

%H Amiram Eldar, <a href="/A354282/b354282.txt">Table of n, a(n) for n = 1..94</a>

%e 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.

%t 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]

%o (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

%Y Subsequence of A006037.

%Y A354283 is a subsequence.

%Y Cf. A005835, A258250, A329190, A354281.

%K nonn

%O 1,1

%A _Amiram Eldar_, May 22 2022