A257691 Numbers that are not A000120-abundant.

1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 25, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 95, 97, 101, 103, 107, 109, 111, 113, 119, 121, 123, 125, 127, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 187, 191, 193, 197, 199, 211, 219, 221, 223, 227, 229, 233, 239, 241, 247, 251, 257

Offset

1,2

Comments

A000120-nonabundant numbers: Numbers n for which A192895(n) <= 0.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Mathematica

A192895[n_] := DivisorSum[n, Total[IntegerDigits[#, 2]]*(-1)^Boole[# == n]& ]; Reap[For[n=1, n<300, n++, If[A192895[n] <= 0, Sow[n]]]][[2, 1]] (* Jean-François Alcover, Dec 05 2015 *)

Prog

(PARI)
A192895(n) = sumdiv(n, d, hammingweight(d)*(-1)^(d==n));
isA257691(n) = (A192895(n) <= 0);
n=i=0; while(i < 10000, n++; if(isA257691(n), i++; write("b257691.txt", i, " ", n))); \\ Charles R Greathouse IV, Feb 07 2013

Crossrefs

Cf. A000120, A192895.

Complement of A175526 (A000120-abundant numbers).

Disjoint union of A175522 (A000120-perfect numbers) and A175524 (A000120-deficient numbers).

Differs from A206074(n-1), A186891(n) and A257688(n) for the first time at n=19, where a(19) = 59, while A206074(18) = A186891(19) = A257688(19) = 55, a term missing from here.

Differs from A257689 for the first time at n=24, where a(24) = 79, while A257689(24) = 77, a term missing from here.

Sequence in context: A325559 A257688 A257689 * A372059 A164574 A344023

Adjacent sequences: A257688 A257689 A257690 * A257692 A257693 A257694

Keyword

nonn

Author

Antti Karttunen, May 11 2015

Status

approved