A228450 Deficient numbers with increasing abundancy without being powers of 2.

3, 9, 10, 44, 110, 136, 592, 884, 2144, 8384, 18632, 32896, 116624, 391612, 527872, 1090912, 2102272, 8394752, 15370304, 73995392, 536920064, 815634435, 2147516416, 34360131584, 217898810368, 546409576448, 549759483904

Offset: 1

Author

Michel Marcus, Oct 27 2013

Keywords

• nonn
• more

Comments

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

Examples

			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.
		

Crossrefs

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

Programs

Mathematica

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 *)

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

Extensions

a(21)-a(22) from Michel Marcus, Oct 28 2013

a(23)-a(27) from Donovan Johnson, Nov 13 2013