A335542 Numbers with a record number of deficient divisors.

1, 2, 4, 8, 16, 30, 60, 90, 150, 210, 315, 630, 990, 1575, 1890, 2310, 3465, 4620, 6930, 11550, 13860, 17325, 20790, 30030, 39270, 45045, 60060, 78540, 90090, 117810, 131670, 180180, 196350, 219450, 225225, 255255, 270270, 353430, 395010, 450450, 510510, 746130

Offset: 1

Author

Amiram Eldar, Jun 13 2020

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..120

Crossrefs

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

Programs

Mathematica

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
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 *)

Formula

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