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A302127 Primitive terms of A067808. 1
720, 1080, 1680, 1800, 2016, 2520, 3024, 3780, 3960, 4200, 4680, 5280, 5544, 6120, 6300, 6840, 7056, 9240, 9504, 9600, 10584, 10920, 11232, 12480, 12672, 13104, 13200, 13860, 14256, 14280, 15600, 16380, 17136, 19152, 19656, 20400, 20592, 21420, 23184, 23940, 24000, 25704, 26928, 28728, 29232 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Terms of A067808 that are not divisible by any smaller term of A067808.
For any set S of primes whose sum of reciprocals is infinite, there are members whose prime factors are all in S. For example, by the strong form of Dirichlet's theorem this is the case for an arithmetic progression {x: x == c (mod d)} if c and d are coprime.
LINKS
MAPLE
count:= 0: Res:= NULL:
for n from 1 while count < 100 do
F:= ifactors(n)[2];
if mul((t[1]^(t[2]+1)-1)^2/(t[1]^(2*t[2]+1)-1)/(t[1]-1), t = F) > 3 and andmap(s -> not(type(n/s, integer)), [Res]) then
count:= count+1; Res:= Res, n;
fi
od:
Res;
MATHEMATICA
count = 0; Res = {};
For[n = 2, count < 100, n++, F = FactorInteger[n]; If[Product[{p, e} = pe; (p^(e+1)-1)^2/((p^(2e+1)-1)(p-1)), {pe, F}] > 3 && AllTrue[Res, !IntegerQ[n/#]&], count++; AppendTo[Res, n]]
];
Res (* Jean-François Alcover, Apr 29 2019, after Robert Israel *)
CROSSREFS
Cf. A067808.
Sequence in context: A137493 A179669 A067808 * A291804 A131663 A090392
KEYWORD
nonn
AUTHOR
Robert Israel, Jun 20 2018
STATUS
approved

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Last modified July 13 02:50 EDT 2024. Contains 374265 sequences. (Running on oeis4.)