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A354282
Weird numbers k such that k+1 is the sum of a subset of the aliquot divisors of k.
3
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
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.
Sequence in context: A364862 A006037 A002975 * A329190 A258250 A349285
KEYWORD
nonn
AUTHOR
Amiram Eldar, May 22 2022
STATUS
approved