A257691 - OEIS

%I #17 Jul 19 2016 15:30:59

%S 1,2,3,5,7,11,13,17,19,23,25,29,31,37,41,43,47,53,59,61,67,71,73,79,

%T 83,89,95,97,101,103,107,109,111,113,119,121,123,125,127,131,137,139,

%U 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

%N Numbers that are not A000120-abundant.

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

%H Antti Karttunen, <a href="/A257691/b257691.txt">Table of n, a(n) for n = 1..10000</a>

%t 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 *)

%o (PARI)

%o A192895(n) = sumdiv(n, d, hammingweight(d)*(-1)^(d==n));

%o isA257691(n) = (A192895(n) <= 0);

%o n=i=0; while(i < 10000, n++; if(isA257691(n), i++; write("b257691.txt", i, " ", n))); \\ _Charles R Greathouse IV_, Feb 07 2013

%Y Cf. A000120, A192895.

%Y Complement of A175526 (A000120-abundant numbers).

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

%Y 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.

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

%K nonn

%O 1,2

%A _Antti Karttunen_, May 11 2015