A335542 - OEIS

%I #13 May 06 2023 16:06:51

%S 1,2,4,8,16,30,60,90,150,210,315,630,990,1575,1890,2310,3465,4620,

%T 6930,11550,13860,17325,20790,30030,39270,45045,60060,78540,90090,

%U 117810,131670,180180,196350,219450,225225,255255,270270,353430,395010,450450,510510,746130

%N Numbers with a record number of deficient divisors.

%C The corresponding numbers of deficient divisors are 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 15, 16, 17, 18, 22, ...

%H Amiram Eldar, <a href="/A335542/b335542.txt">Table of n, a(n) for n = 1..120</a>

%F Numbers m such that A080226(m) > A080226(k) for all k < m.

%e 2 is in the sequence since it is the least number with 2 deficient divisors, 1 and 2. The next number with more than 2 deficient divisors is 4, which has 3 deficient divisors, 1, 2, and 4.

%t s[n_] := Count[Divisors[n], _?(DivisorSigma[1, #] < 2*# &)]; sm = -1; seq = {}; Do[s1 = s[n]; If[s1 > sm, sm = s1; AppendTo[seq, n]], {n, 1, 10^6}]; seq

%t Module[{nn=800000,lst},lst=Table[{n,Count[Divisors[n],_?(DivisorSigma[1,#]<2#&)]},{n,nn}];DeleteDuplicates[lst,GreaterEqual[#1[[2]],#2[[2]]]&]][[;;,1]] (* _Harvey P. Dale_, May 06 2023 *)

%Y Cf. A000203, A005100, A080226, A302934, A335540.

%K nonn

%O 1,2

%A _Amiram Eldar_, Jun 13 2020