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A034287
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Numbers whose product of divisors is larger than that of any smaller number.
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13
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1, 2, 3, 4, 6, 8, 10, 12, 18, 20, 24, 30, 36, 48, 60, 72, 84, 90, 96, 108, 120, 168, 180, 240, 336, 360, 420, 480, 504, 540, 600, 630, 660, 672, 720, 840, 1080, 1260, 1440, 1680, 2160, 2520, 3360, 3780, 3960, 4200, 4320, 4620, 4680, 5040, 7560, 9240
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OFFSET
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1,2
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COMMENTS
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It appears that 2 and 3 are the only terms in this sequence that are not in A034288. - T. D. Noe, Mar 10 2007
a(n) = numbers m where record values occur in A007955(m); A007955(m) = product of divisors of m. a(n) = possible values of A174901(m) in increasing order, a(n) = the smallest numbers k such that A007955(k) = A174899(n). - Jaroslav Krizek, Apr 01 2010
Equals A067128 for the 105834 terms less than 10^150.
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LINKS
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MATHEMATICA
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divProd[n_] := Times @@ Divisors[n]; a[1] = 1; a[n_] := a[n] = Catch[For[dp = divProd[an = a[n - 1]]; an++, True, an++, If[divProd[an] > dp, Throw[an]]]]; Table[a[n], {n, 1, 52}] (* Jean-François Alcover, Feb 01 2013 *)
DeleteDuplicates[Table[{n, Times@@Divisors[n]}, {n, 10000}], GreaterEqual[#1[[2]], #2[[2]]]&] [[;; , 1]] (* Harvey P. Dale, Oct 07 2023 *)
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PROG
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(PARI) A007955(n)=if(issquare(n, &n), n^numdiv(n^2), n^(numdiv(n)/2))
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CROSSREFS
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KEYWORD
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easy,nonn,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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