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%I #5 Jun 05 2020 09:58:33
%S 49,324,1024,1444,1681,2600,9800,265225,332928,379456,421200,1940449,
%T 4198400,4293184,4739328,8346320,11309768,27050400,65918161,203694425,
%U 384199200,418488849,546717924,2239277041,2687489280,4866742025,5783450400,6933892900,7725003664
%N Numbers k such that k and k+1 are both antiharmonic numbers (A020487).
%C Terms of this sequence k such that k and k+1 are both nonsquares (A227771) are 203694425, 4866742025, ...
%C Can two consecutive numbers be both primitive antiharmonic numbers (A228023)? Numbers k such that k and k+2 are both primitive antiharmonic numbers exist - the first two are 38246258 and 344321280.
%e 49 is a term since both 49 and 50 are antiharmonic: sigma_2(49)/sigma(49) = 43 and sigma_2(50)/sigma(50) = 35 are both integers.
%t antihQ[n_] := Divisible[DivisorSigma[2, n], DivisorSigma[1, n]]; seq = {}; q1 = antihQ[1]; Do[q2 = antihQ[n]; If[q1 && q2, AppendTo[seq, n - 1]]; q1 = q2, {n, 2, 2 * 10^6}]; seq
%Y Cf. A000203, A001157, A020487, A227771, A228023.
%K nonn
%O 1,1
%A _Amiram Eldar_, Jun 04 2020
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