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%I #24 Jul 07 2022 16:20:17
%S 1,2,4,6,12,24,36,48,60,120,180,240,360,720,1080,1260,1440,1680,2160,
%T 2520,5040,7560,10080,15120,21840,28080,32760,56160,65520,98280,
%U 131040,196560,393120,589680,786240,1113840,1670760,2227680,3341520,6683040,13366080,20049120
%N Integers whose number of normal undulating divisors sets a new record.
%C Normal undulating integers are in A355301.
%C 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.
%C Corresponding records of number of normal undulating divisors are 1, 2, 3, 4, 6, 8, 9, 10, 12, ...
%e a(6) = 24 is in the sequence because A355302(24) is larger than any earlier value in A355302.
%t 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 *)
%Y Cf. A002182, A355301, A355302, A355303.
%Y Similar, but with divisors that are: A046952 (squares), A053624 (odd), A181808 (even), A093036 (palindromes), A340548 (repdigits), A340549 (repunits), A350756 (triangular).
%K nonn,base
%O 1,2
%A _Bernard Schott_, Jun 30 2022
%E More terms from _Amiram Eldar_, Jun 30 2022
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