A181629 Positive integers k = p_1^{r_1} ... p_n^{r_n} such that sum_{i=1..n} p_i^{-r_i} >= 1 (Non-Hyperbolic Integers).

1, 30, 210, 330, 390, 462, 510, 546, 570, 690, 714, 798, 858, 870, 930, 966, 1050, 1110, 1218, 1230, 1290, 1302, 1410, 1470, 1554, 1590, 1722, 1770, 1830, 2010, 2130, 2190, 2310, 2370, 2490, 2670, 2730, 2910, 3030, 3090, 3210, 3270, 3390, 3570, 3630, 3810

Offset: 1

Author

Roberto E. Martinez II, Nov 02 2010, Nov 05 2010

Keywords

• nonn

Comments

First odd term greater than 1 is 3234846615. - Robert G. Wilson v, Nov 04 2010

Also numbers n such that A028236(n)/n >= 1. - Klaus Brockhaus, Nov 06 2010

Examples

			a(2) = 30, since 30 = 2*3*5 and 1/2 + 1/3 + 1/5 = 31/30 >= 1.
		

Crossrefs

Cf. A028236 (if n = Product (p_j^k_j), a(n) = numerator of Sum 1/p_j^k_j). - Klaus Brockhaus, Nov 06 2010

Programs

Magma

[1] cat [ k: k in [2..4000] | &+[ f[i, 1]^-f[i, 2]: i in [1..#f] ] ge 1 where f is Factorization(k) ]; // Klaus Brockhaus, Nov 06 2010

Mathematica

DeleteCases[ Table[k; A = FactorInteger[k]; If[Sum[1/A[[j]][[1]]^A[[j]][[2]], {j, 1, Length[A]}] >= 1, k, 0], {k, 1, 3900}], 0]
fQ[n_] := Block[{fi = Transpose@ FactorInteger@ n}, Plus @@ (1/(First@fi ^ Last@fi)) >= 1]; Select[Range@ 3900, fQ] (* Robert G. Wilson v, Nov 04 2010 *)