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A288453 Weird totient numbers: totient abundant numbers (A286265) that are not pseudoperfect totient numbers (A288452). 0
91, 95, 133, 145, 185, 203, 215, 217, 259, 275, 301, 335, 343, 355, 365, 395, 427, 469, 497, 545, 551, 553, 575, 635, 637, 649, 655, 703, 725, 755, 763, 767, 785, 815, 817, 833, 865, 889, 893, 905, 917, 931, 949, 955, 973, 985, 995, 1007, 1027, 1057, 1073 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Analogous to A006037 (weird numbers) as A082897 (perfect totient numbers) is analogous to A000396 (perfect numbers).

LINKS

Table of n, a(n) for n=1..51.

EXAMPLE

The set of iterated phi of 91 is {72, 24, 8, 4, 2, 1} and none of its subsets sums to 91.

MATHEMATICA

pseudoPerfectTotQ[n_] := Module[{tots = Most[Rest[FixedPointList[EulerPhi@# &, n]]]}, MemberQ[Total /@ Subsets[tots, Length[tots]], n]];

totAbundantQ[n_] := Plus @@ FixedPointList[EulerPhi@# &, n] > 2*n + 1;

weirdTotient[n_] := totAbundantQ[n] && ! pseudoPerfectTotQ[n];

Select[Range[1100], weirdTotient]

CROSSREFS

Cf. A000010, A000396, A006037, A092693, A082897, A286265.

Sequence in context: A020318 A126134 A020223 * A184034 A294742 A224981

Adjacent sequences:  A288450 A288451 A288452 * A288454 A288455 A288456

KEYWORD

nonn

AUTHOR

Amiram Eldar, Jun 09 2017

STATUS

approved

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Last modified November 14 04:40 EST 2019. Contains 329108 sequences. (Running on oeis4.)