A343330 - OEIS

%I #11 Apr 24 2021 21:36:35

%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,945,0,0,2205,0,0,2835,0,0,15435,0,0,

%T 8505,0,0,108045,0,0,11025,25515,0,46305,0,0,756315,0,0,81675,76545,0,

%U 324135,0,0,5294205,0,0,540225,229635,0,2268945,0,0,898425,37059435,0,972405,0,3781575,688905,0,0,15882615,0

%N a(n) is the largest odd positive integer that is abundant and has the same prime signature as A279537(n) or 0 if no such integer exists.

%C Odd abundant numbers k have omega(k) >= 3. The zeros in this sequence come from numbers k having omega(k) < 3 in which case no positive integer with that prime signature exists.

%C Numbers with omega(k) > 3 are excluded by definition as most such numbers have infinitely many cases for that prime signature in which case no largest element exists.

%e a(17) = 945 as A279537(17) = 120 = 2^(3) * 3^(1) * 5^(1) and has prime signature (3, 1, 1). The largest odd positive integer that has prime signature (3, 1, 1) and is abundant is 945.

%K nonn

%O 1,17

%A _David A. Corneth_, Apr 12 2021