A355304 Integers whose number of normal undulating divisors sets a new record.

1, 2, 4, 6, 12, 24, 36, 48, 60, 120, 180, 240, 360, 720, 1080, 1260, 1440, 1680, 2160, 2520, 5040, 7560, 10080, 15120, 21840, 28080, 32760, 56160, 65520, 98280, 131040, 196560, 393120, 589680, 786240, 1113840, 1670760, 2227680, 3341520, 6683040, 13366080, 20049120

Offset

1,2

Comments

Normal undulating integers are in A355301.

The first 14 terms are also the first 14 highly composite numbers in A002182, then A002182(15) = 840 while a(15) = 1080. Indeed, 840 is the smallest integer that has 32 divisors of which only 28 are normal undulating integers, while 1080 has also 32 divisors of which 30 are normal undulating integers.

Corresponding records of number of normal undulating divisors are 1, 2, 3, 4, 6, 8, 9, 10, 12, ...

Links

Table of n, a(n) for n=1..42.

Example

a(6) = 24 is in the sequence because A355302(24) is larger than any earlier value in A355302.

Mathematica

nuQ[n_] := AllTrue[(s = Sign[Differences[IntegerDigits[n]]]), # != 0 &] && AllTrue[Differences[s], # != 0 &]; dm = -1; seq = {}; Do[If[(d = DivisorSum[n, 1 &, nuQ[#] &]) > dm, dm = d; AppendTo[seq, n]], {n, 1, 10^5}]; seq (* Amiram Eldar, Jun 30 2022 *)

Crossrefs

Cf. A002182, A355301, A355302, A355303.

Similar, but with divisors that are: A046952 (squares), A053624 (odd), A181808 (even), A093036 (palindromes), A340548 (repdigits), A340549 (repunits), A350756 (triangular).

Sequence in context: A166981 A004394 A189686 * A137425 A141320 A307122

Adjacent sequences: A355301 A355302 A355303 * A355305 A355306 A355307

Keyword

nonn,base

Author

Bernard Schott, Jun 30 2022

Extensions

More terms from Amiram Eldar, Jun 30 2022

Status

approved