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A190641
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Numbers having exactly one non-unitary prime factor.
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17
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4, 8, 9, 12, 16, 18, 20, 24, 25, 27, 28, 32, 40, 44, 45, 48, 49, 50, 52, 54, 56, 60, 63, 64, 68, 75, 76, 80, 81, 84, 88, 90, 92, 96, 98, 99, 104, 112, 116, 117, 120, 121, 124, 125, 126, 128, 132, 135, 136, 140, 147, 148, 150, 152, 153, 156, 160, 162, 164
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OFFSET
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1,1
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COMMENTS
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A056170(a(n)) = 1.
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Vaclav Kotesovec, Graph - the asymptotic ratio
Carl Pomerance, Andrzej Schinzel, Multiplicative Properties of Sets of Residues, Moscow Journal of Combinatorics and Number Theory. 2011. Vol. 1. Iss. 1. pp. 52-66. See p. 61.
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FORMULA
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a(n) ~ k*n, where k = Pi^2/(6*A154945) = 2.9816096.... - Charles R Greathouse IV, Aug 02 2016
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MATHEMATICA
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Select[Range[164], Count[FactorInteger[#][[All, 2]], 1] == Length[FactorInteger[#]] - 1 &] (* Geoffrey Critzer, Feb 05 2015 *)
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PROG
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(Haskell)
a190641 n = a190641_list !! (n-1)
a190641_list = map (+ 1) $ elemIndices 1 a056170_list
(PARI) list(lim)=my(s=lim\4, v=List(), u=vectorsmall(s, i, 1), t, x); forprime(k=2, sqrtint(s), t=k^2; forstep(i=t, s, t, u[i]=0)); forprime(k=2, sqrtint(lim\1), for(e=2, logint(lim\1, k), t=k^e; for(i=1, #u, if(u[i] && gcd(k, i)==1, x=t*i; if(x>lim, break); listput(v, x))))); Set(v) \\ Charles R Greathouse IV, Aug 02 2016
(PARI) isok(n) = my(f=factor(n)); #select(x->(x>1), f[, 2]) == 1; \\ Michel Marcus, Jul 30 2017
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CROSSREFS
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Subsequence of A013929 and of A327877.
Sequence in context: A162966 A350137 A359470 * A327877 A359468 A034043
Adjacent sequences: A190638 A190639 A190640 * A190642 A190643 A190644
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller, Dec 29 2012
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STATUS
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approved
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