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A308532
Highly composite numbers (A002182) with a record number of largely composite numbers (A067128) having the same number of divisors.
1
1, 2, 6, 60, 360, 73513440, 1396755360, 4497552259200, 130429015516800, 149602080797769600, 4488062423933088000, 6133685312708553600, 184010559381256608000, 7912454053394034144000, 19709923047004539052704000, 1162885459773267804109536000, 780296143507862696557498656000
OFFSET
1,2
COMMENTS
The corresponding record numbers of divisors d(a(n)) are 1, 2, 3, 6, 9, 10, 11, 14, 16, 20, ... (see the link for more values).
EXAMPLE
6 is in the sequence since there are a record number of 3 largely composite numbers, 6, 8, and 10 with the same number of divisors. The next record is of 60, with 6 largely composite numbers, 60, 72, 84, 90, 96, and 108, with the same number of divisors.
MATHEMATICA
s = {}; dm = 1; c = 0; cm = 0; nprev = 1; Do[d = DivisorSigma[0, n]; If[d == dm, c++]; If[d > dm, dm = d; If[c > cm, cm = c; AppendTo[s, nprev]]; c = 1; nprev = n], {n, 1, 10^3}]; s
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Jun 06 2019
STATUS
approved