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A034287
Numbers whose product of divisors is larger than that of any smaller number.
13
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
OFFSET
1,2
COMMENTS
It appears that 2 and 3 are the only terms in this sequence that are not in A034288. - T. D. Noe, Mar 10 2007
Is this the same as A067128?
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.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..230 (terms below 10^10, terms 1..161 from T. D. Noe)
MATHEMATICA
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 *)
PROG
(PARI) A007955(n)=if(issquare(n, &n), n^numdiv(n^2), n^(numdiv(n)/2))
r=0; for(n=1, 1e5, t=A007955(n); if(t>r, r=t; print1(n", "))) \\ Charles R Greathouse IV, Feb 01 2013
CROSSREFS
KEYWORD
easy,nonn,nice
EXTENSIONS
More terms from David W. Wilson, Dec 19 2001
STATUS
approved