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A190641
Numbers having exactly one non-unitary prime factor.
23
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
OFFSET
1,1
COMMENTS
Numbers k such that the powerful part of k, A057521(k), is a composite prime power (A246547). - Amiram Eldar, Aug 01 2024
LINKS
Vaclav Kotesovec, Graph - the asymptotic ratio.
Carl Pomerance and Andrzej Schinzel, Multiplicative Properties of Sets of Residues, Moscow Journal of Combinatorics and Number Theory, Vol. 1, Iss. 1 (2011), pp. 52-66. See p. 61.
FORMULA
A056170(a(n)) = 1.
a(n) ~ k*n, where k = Pi^2/(6*A154945) = 2.9816096.... - Charles R Greathouse IV, Aug 02 2016
MATHEMATICA
Select[Range[164], Count[FactorInteger[#][[All, 2]], 1] == Length[FactorInteger[#]] - 1 &] (* Geoffrey Critzer, Feb 05 2015 *)
PROG
(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
CROSSREFS
Subsequence of A013929 and of A327877.
Cf. A056170, A057521, A154945, A246547, A359466 (characteristic function).
Sequence in context: A375142 A350137 A359470 * A327877 A359468 A034043
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Dec 29 2012
STATUS
approved