A294930 - OEIS

%I #14 Mar 18 2024 03:25:01

%S 0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,

%T 0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,

%U 0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0

%N Characteristic function for A091191, primitive abundant numbers: abundant numbers (A005101) having no abundant proper divisor.

%H Antti Karttunen, <a href="/A294930/b294930.txt">Table of n, a(n) for n = 1..67004</a>

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>.

%F a(n) = A294937(n) * [0==A294929(n)].

%F a(n) = 1 iff A080224(n) = 1.

%t a[n_] := Boole[Count[Divisors[n], _?(DivisorSigma[1, #] > 2*# &)] == 1]; Array[a, 100] (* _Amiram Eldar_, Mar 18 2024 *)

%o (PARI)

%o A294937(n) = (sigma(n)>(2*n));

%o A294929(n) = sumdiv(n, d, (d<n)*A294937(d));

%o A294930(n) = (A294937(n)*(0==A294929(n)));

%Y Cf. A005101, A080224, A091191, A187795, A294890, A294929, A294937.

%K nonn

%O 1

%A _Antti Karttunen_, Nov 14 2017