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%I #26 Jul 23 2021 02:08:32
%S 46,284,1633,149728,242656,260495,298057,1056752,9587584,17706256,
%T 914429696,985501822,1074266048,1484820224,4241800921,12147056128,
%U 109548719577,287291764736,360499817799
%N Numbers k such that the deficiency of k^2 is itself a square > 1.
%C The sequence of square roots of the deficiencies of this sequence is A288144.
%C The disjoint union of the current sequence with the powers of 2 (A000079) is A289275, the sequence of numbers k for which the deficiency of k^2 is a square (including 1).
%e The deficiency of 46^2 is 2*46^2 - sigma(46^2) = 19^2, so 46 is a term of the sequence.
%p issq := n -> evalb(n>1 and issqr(n)):
%p A033879 := n -> 2*n - numtheory[sigma](n):
%p isa := n -> issq(A033879(n^2)):
%p select(isa, [$1..2000]); # _Peter Luschny_, Jul 25 2017
%o (PARI) isok(n) = issquare(d = 2*n^2 - sigma(n^2)) && (d!=1); \\ _Michel Marcus_, Jul 25 2017
%Y Cf. A000079, A033879, A288144, A289275.
%K nonn,more
%O 1,1
%A _Jens Voß_, Jun 30 2017
%E a(10) from _Chai Wah Wu_, Jul 26 2017
%E a(11)-a(19) from _Giovanni Resta_, Jul 27 2017
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