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A190641 Numbers having exactly one non-unitary prime factor. 14
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A056170(a(n)) = 1.

LINKS

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.

FORMULA

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.

Sequence in context: A289553 A013929 A162966 * A327877 A034043 A278517

Adjacent sequences:  A190638 A190639 A190640 * A190642 A190643 A190644

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Dec 29 2012

STATUS

approved

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Last modified November 26 21:20 EST 2020. Contains 338641 sequences. (Running on oeis4.)