A190641 Numbers having exactly one non-unitary prime factor.

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

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: A162966 A350137 A359470 * A327877 A359468 A034043

Adjacent sequences: A190638 A190639 A190640 * A190642 A190643 A190644

Keyword

nonn

Author

Reinhard Zumkeller, Dec 29 2012

Status

approved