OFFSET
1,1
COMMENTS
Alternatively, numbers of the form prime(prime(i))^prime(j) for some positive integers i, j.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
The terms together with their prime indices begin:
9: {2,2}
25: {3,3}
27: {2,2,2}
121: {5,5}
125: {3,3,3}
243: {2,2,2,2,2}
289: {7,7}
961: {11,11}
1331: {5,5,5}
1681: {13,13}
2187: {2,2,2,2,2,2,2}
3125: {3,3,3,3,3}
3481: {17,17}
4489: {19,19}
4913: {7,7,7}
6889: {23,23}
11881: {29,29}
16129: {31,31}
24649: {37,37}
29791: {11,11,11}
MAPLE
N:= 10^7: # for terms <= N
M:=numtheory:-pi(numtheory:-pi(isqrt(N))):
PP:= {seq(ithprime(ithprime(i)), i=1..M)}:
R:= NULL:
for p in PP do
q:= 1:
do
q:= nextprime(q);
t:= p^q;
if t > N then break fi;
R:= R, t;
od;
od:
sort([R]); # Robert Israel, Dec 08 2022
MATHEMATICA
Select[Range[10000], PrimePowerQ[#]&&MatchQ[FactorInteger[#], {{_?(PrimeQ[PrimePi[#]]&), k_?PrimeQ}}]&]
PROG
(Python)
from sympy import primepi, integer_nthroot, primerange
def A352519(n):
def f(x): return int(n+x-sum(primepi(primepi(integer_nthroot(x, p)[0])) for p in primerange(x.bit_length())))
def bisection(f, kmin=0, kmax=1):
while f(kmax) > kmax: kmax <<= 1
while kmax-kmin > 1:
kmid = kmax+kmin>>1
if f(kmid) <= kmid:
kmax = kmid
else:
kmin = kmid
return kmax
return bisection(f, n, n) # Chai Wah Wu, Sep 12 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 26 2022
STATUS
approved