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Deficient numbers with increasing abundancy without being powers of 2.
5

%I #25 Apr 07 2021 03:06:46

%S 3,9,10,44,110,136,592,884,2144,8384,18632,32896,116624,391612,527872,

%T 1090912,2102272,8394752,15370304,73995392,536920064,815634435,

%U 2147516416,34360131584,217898810368,546409576448,549759483904

%N Deficient numbers with increasing abundancy without being powers of 2.

%C Without the additional condition one would have obtained A000079, see "least deficient" comment there. Subsequence of A005100.

%e First term is 3 with sigma(n)/n = 4/3 ~ 1.33, then 4 with 13/9 ~ 1.44, then 10 with 9/5 = 1.80.

%t abun[n_] := DivisorSigma[1, n]/n; mx = 0; t = {}; Do[m = abun[n]; If[m < 2 && m > mx && ! IntegerQ[Log[2, n]], mx = m; AppendTo[t, n]], {n, 10000}]; t (* _T. D. Noe_, Apr 09 2014 *)

%o (PARI) lista(nn) = {rab = 0; for (n=1, nn, if (n != 2^valuation(n, 2), ab = sigma(n)/n; if ((ab < 2) && (ab > rab), print1(n, ", "); rab = ab;);););} \\ _Michel Marcus_, Oct 27 2013

%Y Cf. A000079, A000203, A005100, A071927, A171929, A188597.

%K nonn,more

%O 1,1

%A _Michel Marcus_, Oct 27 2013

%E a(21)-a(22) from _Michel Marcus_, Oct 28 2013

%E a(23)-a(27) from _Donovan Johnson_, Nov 13 2013