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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). 2
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 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn
AUTHOR
Roberto E. Martinez II, Nov 02 2010, Nov 05 2010
STATUS
approved

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Last modified April 14 18:28 EDT 2024. Contains 371667 sequences. (Running on oeis4.)