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%I #29 Oct 07 2023 11:53:01
%S 1,2,3,4,6,8,10,12,18,20,24,30,36,48,60,72,84,90,96,108,120,168,180,
%T 240,336,360,420,480,504,540,600,630,660,672,720,840,1080,1260,1440,
%U 1680,2160,2520,3360,3780,3960,4200,4320,4620,4680,5040,7560,9240
%N Numbers whose product of divisors is larger than that of any smaller number.
%C It appears that 2 and 3 are the only terms in this sequence that are not in A034288. - _T. D. Noe_, Mar 10 2007
%C Is this the same as A067128?
%C 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
%C Equals A067128 for the 105834 terms less than 10^150.
%H Amiram Eldar, <a href="/A034287/b034287.txt">Table of n, a(n) for n = 1..230</a> (terms below 10^10, terms 1..161 from T. D. Noe)
%t 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 *)
%t DeleteDuplicates[Table[{n,Times@@Divisors[n]},{n,10000}],GreaterEqual[#1[[2]],#2[[2]]]&] [[;;,1]] (* _Harvey P. Dale_, Oct 07 2023 *)
%o (PARI) A007955(n)=if(issquare(n, &n), n^numdiv(n^2), n^(numdiv(n)/2))
%o r=0;for(n=1,1e5,t=A007955(n);if(t>r,r=t;print1(n", "))) \\ _Charles R Greathouse IV_, Feb 01 2013
%Y Cf. A007955, A007956, A034288, A034090, A034091, A067128.
%K easy,nonn,nice
%O 1,2
%A _Erich Friedman_
%E More terms from _David W. Wilson_, Dec 19 2001
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