login
A335542
Numbers with a record number of deficient divisors.
2
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
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
KEYWORD
nonn
AUTHOR
Amiram Eldar, Jun 13 2020
STATUS
approved