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A069875
Smallest multiple of n with a prime signature different from all previous terms.
1
1, 2, 6, 4, 20, 24, 42, 8, 36, 60, 176, 72, 312, 210, 180, 16, 544, 144, 912, 320, 420, 792, 2208, 216, 800, 1560, 243, 896, 4176, 900, 5580, 64, 2112, 3570, 1680, 432, 7992, 4864, 3744, 1600, 14760, 2688, 18060, 4752, 1800, 11040, 24064, 864, 6272, 3600
OFFSET
1,2
LINKS
EXAMPLE
a(1) through a(4) have prime signatures 0, 1, (1, 1) and 2. a(5) = 20 because 5 has prime signature 1, which has already been used and 10 and 15 have prime signature (1, 1), which has already been used, but 20 has prime signature (2, 1), which has not yet been used.
MATHEMATICA
lps[n_] := Module[{e = ReverseSort[FactorInteger[n][[;; , 2]]]}, Times @@ (Prime[Range[Length[e]]]^e)]; lps[1] = 1; seq[nmax_] := Module[{v = {}, s = Table[0, {nmax}], k}, Do[k = n; While[MemberQ[v, lps[k]], k += n]; AppendTo[v, lps[k]]; s[[n]] = k, {n, 1, nmax}]; s]; seq[50] (* Amiram Eldar, Jul 27 2024 *)
CROSSREFS
Sequence in context: A309243 A112326 A075435 * A202962 A019088 A096085
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Apr 25 2002
EXTENSIONS
More terms from David Wasserman, Apr 30 2003
STATUS
approved