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

1,1

Comments

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

Links

Table of n, a(n) for n=1..27.

Example

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.

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A173242 A335030 A335029 * A121057 A025538 A070354

Adjacent sequences: A228447 A228448 A228449 * A228451 A228452 A228453

Keyword

nonn,more

Author

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

Status

approved