A034287 Numbers whose product of divisors is larger than that of any smaller number.

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

Author

Erich Friedman

Keywords

• easy
• nonn
• nice

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)

Crossrefs

Cf. A007955, A007956, A034288, A034090, A034091, A067128.

Programs

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 *)

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

Extensions

More terms from David W. Wilson, Dec 19 2001