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A354281
Weird numbers k such that k-1 is the sum of a subset of the aliquot divisors of k.
3
70, 4030, 5830, 9272, 17272, 243892, 351956, 407132, 1901728, 2189024, 4199030, 11339816, 11547352, 12872512, 13885970, 24450010, 31699430, 32284330, 34041370, 34169630, 34315712, 38546576, 42251930, 50761810, 67727110, 67820390, 68000392, 72986296, 85389368
OFFSET
1,1
COMMENTS
There are 17270452 weird numbers below 10^10 and only 68 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 69 = 1 + 2 + 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}]; c = SeriesCoefficient[s, #] & /@ (n + {-1, 0}); 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: A306984 A292986 A064114 * A348631 A354283 A319735
KEYWORD
nonn
AUTHOR
Amiram Eldar, May 22 2022
STATUS
approved