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

1,2

Comments

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

Links

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

Formula

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

Example

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.

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 *)

Crossrefs

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

Sequence in context: A164259 A164203 A164178 * A027423 A140410 A213368

Adjacent sequences: A335539 A335540 A335541 * A335543 A335544 A335545

Keyword

nonn

Author

Amiram Eldar, Jun 13 2020

Status

approved