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

1,2

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

Links

Table of n, a(n) for n=1..46.

Example

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

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 *)

Prog

(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

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

Sequence in context: A280482 A371721 A203617 * A346245 A129499 A286763

Adjacent sequences: A181626 A181627 A181628 * A181630 A181631 A181632

Keyword

nonn

Author

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

Status

approved