A051774 Contracted numbers.

6, 12, 18, 20, 24, 28, 30, 36, 40, 42, 45, 48, 54, 56, 60, 63, 66, 70, 72, 78, 80, 84, 88, 90, 96, 99, 100, 102, 104, 105, 108, 110, 112, 114, 117, 120, 126, 130, 132, 135, 138, 140, 144, 150, 154, 156, 160, 162, 165, 168, 170, 174, 175, 176, 180, 182, 186

Offset

1,1

Comments

n is said to be contracted if and only if n has distinct divisors d_1 < d_2 < ... < d_k such that d_1+d_2+...+d_(k-1) >= d_k. Note that d_k need not be the greatest divisor of n -- see the examples.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Example

6 has divisors 1, 2, 3, 6, and 1+2 >= 3, so 6 is a member. 45 has divisors 1, 3, 5, 9, 15, 45, and 1+3+5+9 = 18 > 15, so 45 is a member. - N. J. A. Sloane, Jun 12 2021

Mathematica

cnQ[n_]:=Module[{d=Divisors[n], len}, len=Length[d]; AnyTrue[Table[Take[ d, k], {k, 3, len}], Total[Most[#]]>=Last[#]&]]; Select[Range[200], cnQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 12 2021 *)

Crossrefs

Numbers not in A051772.

Sequence in context: A105289 A328608 A328671 * A119357 A097216 A346695

Adjacent sequences: A051771 A051772 A051773 * A051775 A051776 A051777

Keyword

nonn

Author

Alexander Benjamin Schwartz (QBOB(AT)aol.com), Dec 08 1999

Status

approved