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 A308531 Largely composite numbers (A067128) with a unique number of divisors. 1
 1, 4, 36, 48, 180, 720, 5040, 20160, 25200, 45360, 50400, 498960, 665280, 3603600, 6486480, 7207200, 8648640, 14414400, 32432400, 110270160, 698377680, 2095133040, 2205403200, 41902660800, 73329656400, 146659312800, 240940299600, 293318625600, 963761198400 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS These are highly composite numbers (A002182) that have no other largely composite numbers with the same number of divisors. The corresponding numbers of divisors d(a(n)) are 1, 3, 9, 10, 18, 30, 60, 84, 90, 100, ... (see the link for more values). LINKS Amiram Eldar, Table of n, a(n) for n = 1..114 Amiram Eldar, Table of n, a(n), d(a(n)) for n = 1..114 FORMULA A002182(k) is in the sequence if A308530(k) = 1. EXAMPLE 4 is in the sequence since it is the only largely composite number with 3 divisors. 2 is not in the sequence since it has 2 divisors, the same as the next largely composite number 3. MATHEMATICA s = {}; dm = 1; c = 0; nprev = 1; Do[d = DivisorSigma[0, n]; If[d == dm, c++]; If[d > dm, dm = d; If[c == 1, AppendTo[s, nprev]]; c = 1; nprev = n], {n, 1, 10^8}]; s CROSSREFS Cf. A000005, A002182, A067128, A308530. Sequence in context: A327998 A274891 A062182 * A073771 A219247 A224094 Adjacent sequences:  A308528 A308529 A308530 * A308532 A308533 A308534 KEYWORD nonn AUTHOR Amiram Eldar, Jun 06 2019 STATUS approved

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Last modified August 14 10:47 EDT 2020. Contains 336480 sequences. (Running on oeis4.)