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A326677
Numbers with a record number of divisors, counted with multiplicity (A169594).
2
1, 2, 4, 8, 12, 16, 24, 32, 36, 48, 64, 72, 96, 120, 144, 240, 288, 360, 432, 576, 720, 1080, 1260, 1440, 2160, 2520, 2880, 3600, 5040, 7200, 7560, 8640, 10080, 14400, 15120, 20160, 25200, 30240, 40320, 45360, 50400, 55440, 75600, 100800, 110880, 151200, 166320
OFFSET
1,2
COMMENTS
The corresponding record values are 1, 2, 4, 6, 7, 9, 10, 11, 12, 14, 15, 16, 17, 18, 22, 24, 26, 28, 29, ...
Since the value of A169594(k) depends only on the prime signature of k, this sequence is a subsequence of A025487.
LINKS
EXAMPLE
The first values of A169594(n) for n=1..8 are {1, 2, 2, 4, 2, 4, 2, 6}. The record values are 1, 2, 4, 6, for 1, 2, 4, 8. Therefore this sequence begins with 1, 2, 4, 8.
MATHEMATICA
d[n_]:=1 + DivisorSum[n, IntegerExponent[n, #] &, # > 1 &]; s={}; dm = 0; Do[d1 = d[n]; If[d1 > dm, dm = d1; AppendTo[s, n]], {n, 1, 10000}]; s (* after Michael De Vlieger at A169594 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Oct 18 2019
STATUS
approved