

A034287


Numbers n such that product of divisors of n is larger than for any number less than n.


12



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

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}] (* JeanFrançois Alcover, Feb 01 2013 *)


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

Cf. A007955, A007956, A034288, A034090, A034091, A067128.
Sequence in context: A213623 A074715 A216365 * A067128 A245779 A120432
Adjacent sequences: A034284 A034285 A034286 * A034288 A034289 A034290


KEYWORD

easy,nonn,nice


AUTHOR

Erich Friedman


EXTENSIONS

More terms from David W. Wilson, Dec 19 2001


STATUS

approved



