A349868 - OEIS

%I #11 Dec 06 2021 03:11:55

%S 315,495,525,585,675,693,735,765,819,825,850,855,884,950,975,988,1012,

%T 1035,1071,1078,1125,1150,1196,1197,1210,1215,1274,1275,1276,1287,

%U 1292,1305,1323,1364,1395,1425,1449,1450,1508,1550,1564,1612,1617,1628,1665,1666

%N Nobly abundant numbers (A349758) that are not abundant numbers (A005101).

%C This sequence if infinite. For example, 45*p is a term if p is a prime > 5.

%H Amiram Eldar, <a href="/A349868/b349868.txt">Table of n, a(n) for n = 1..10000</a>

%e 315 is a term since it is not abundant, A000203(315) = 624 < 2*315 = 630, and both A000005(315) = 12 and A000203(315) = 624 are abundant numbers.

%t abQ[n_] := DivisorSigma[1, n] > 2*n; nobAbQ[n_] := And @@ abQ /@ DivisorSigma[{0, 1}, n]; Select[Range[2000], !abQ[#] && nobAbQ[#] &]

%Y Intersection of A263837 and A349758.

%Y Cf. A000005, A000203, A005101, A349869.

%K nonn

%O 1,1

%A _Amiram Eldar_, Dec 03 2021