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
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
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
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Dec 29 2012
STATUS
approved