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A064114 Unitary weird numbers: unitary abundant (A034683) but not unitary pseudoperfect (A293188). 5
70, 4030, 5390, 5830, 10430, 10570, 10990, 11410, 11690, 11830, 12110, 12530, 12670, 13370, 13510, 13790, 13930, 14770, 15610, 15890, 16030, 16310, 16730, 16870, 17010, 17570, 17990, 18410, 18830, 18970, 19390, 19670, 19810, 20230, 20510, 21490, 21770, 21910 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Terms that are not (regular) weird (A006037): 5390, 11830, 17010, 20230, 25270, 37030, 51030, 58870, 67270, 93170, 95830, ... (* Amiram Eldar, Dec 01 2018 *)

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..205 (terms below 10^5)

EXAMPLE

70 is in the sequence since the sum of its proper unitary divisors, 1, 2, 5, 7, 10, 14, 35 is 74 > 70, yet no subset of these divisors has the sum 74.

MATHEMATICA

udiv[n_] := Select[Divisors[n], GCD[#, n/#] == 1 &]; weirdQ[n_] := Module[{d = Most[udiv[n]]}, If[Total[d] < n, False, c = SeriesCoefficient[Series[Product[1 + x^d[[i]], {i, Length[d]}], {x, 0, n}], n]; c == 0]]; Select[Range[100000], weirdQ] (* Amiram Eldar, Dec 01 2018 *)

CROSSREFS

Cf. A006037, A034683, A293188.

Sequence in context: A275295 A306984 A292986 * A319735 A258374 A146349

Adjacent sequences:  A064111 A064112 A064113 * A064115 A064116 A064117

KEYWORD

nonn

AUTHOR

Naohiro Nomoto, Sep 08 2001

EXTENSIONS

a(25)-a(38) from Amiram Eldar, Dec 01 2018

STATUS

approved

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Last modified October 16 16:18 EDT 2019. Contains 328101 sequences. (Running on oeis4.)