A051283 Numbers k such that if one writes k = Product p_i^e_i (p_i primes) and P = max p_i^e_i, then k/P > P.

30, 60, 70, 84, 90, 105, 120, 126, 132, 140, 154, 165, 168, 180, 182, 195, 198, 210, 220, 231, 234, 252, 260, 264, 273, 280, 286, 306, 308, 312, 315, 330, 336, 340, 357, 360, 364, 374, 380, 385, 390, 396, 399, 408, 418, 420, 429, 440, 442, 455, 456, 462

Offset: 1

Author

Leroy Quet

Keywords

• nonn
• easy
• nice

Comments

Numbers k such that A346418(k) > 1 (conjectured). - Amiram Eldar, Jul 16 2021

Numbers k for which A354933(k) > A034699(k), i.e., where A354995(k) > 0 (conjectured).- Antti Karttunen, Jun 19 2022

Examples

			120 = 2^3*3^1*5^1, P = 2^3 = 8. 120 is included because 120/8 = 15 > 8.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A034699, A080170, A110612, A346418, A354933, A354995, A354996 (characteristic function).

Programs

Haskell

a051283 n = a051283_list !! (n-1)
a051283_list = filter (\x -> (a034699 x) ^ 2 < x) [1..]
-- Reinhard Zumkeller, May 30 2013

Mathematica

ok[n_] := n > Max[Power @@@ FactorInteger[n]]^2; Select[Range[465], ok] (* Jean-François Alcover, Apr 11 2011 *)

PARI

lista(nn) = for(k=2, nn, f=factor(k); if(k>vecmax(vector(#f[, 1], i, f[i, 1]^f[i, 2]))^2, print1(k, ", "))); \\ Jinyuan Wang, Feb 28 2020

Formula

a(n) = A080170(n) + 1 (conjectured). - Ralf Stephan, Feb 20 2004

Extensions

More terms from James Sellers, Dec 11 1999