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A278253
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Least number with the prime signature of the n-th triangular number.
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10
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1, 2, 6, 6, 6, 6, 12, 36, 12, 6, 30, 30, 6, 30, 120, 24, 12, 12, 30, 210, 30, 6, 60, 180, 12, 24, 120, 30, 30, 30, 48, 240, 30, 30, 420, 60, 6, 30, 420, 60, 30, 30, 30, 420, 60, 6, 120, 360, 36, 60, 210, 30, 24, 120, 420, 420, 30, 6, 210, 210, 6, 60, 1440, 480, 210, 30, 30, 210, 210, 30, 180, 180, 6, 60, 420, 210, 210, 30, 120, 2160, 48, 6, 210, 2310, 30, 30
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OFFSET
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1,2
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LINKS
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FORMULA
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MATHEMATICA
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Table[Times @@ MapIndexed[(Prime@ First@ #2)^#1 &, #] &@ If[Length@ # == 1 && #[[1, 1]] == 1, {0}, Reverse@ Sort@ #[[All, -1]]] &@ FactorInteger[ (n^2 - n)/2], {n, 2, 87}] (* Michael De Vlieger, Nov 21 2016 *)
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PROG
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(PARI) a(n)=my(f=vecsort(factor(n*(n+1)/2)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]) \\ Charles R Greathouse IV, Feb 03 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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