login
A217908
Semiprime powers of distinct semiprimes.
1
1296, 4096, 6561, 10000, 38416, 50625, 194481, 234256, 262144, 390625, 456976, 531441, 1000000, 1048576, 1185921, 1336336, 1500625, 2085136, 2313441, 4477456, 5764801, 6765201, 7529536, 9150625, 10077696, 10556001, 11316496, 11390625, 14776336, 17850625
OFFSET
1,1
COMMENTS
Subset of A113877.
LINKS
Christian N. K. Anderson, Table of n, a(n) for n = 1..9006, for a(n) < 1.5*10^18
EXAMPLE
6561=9^4, and 9 and 4 are both semiprime. 46656 = 6^6 is excluded because the semiprimes are not distinct.
PROG
(Python)
from math import isqrt
from sympy import primepi, primerange, integer_nthroot, factorint
def A217908(n):
def A072000(n): return int(-((t:=primepi(s:=isqrt(n)))*(t-1)>>1)+sum(primepi(n//p) for p in primerange(s+1)))
def f(x): return int(n+x-sum(A072000(integer_nthroot(x, p)[0])-(p**p<=x) for p in range(4, x.bit_length()) if sum(factorint(p).values())==2))
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
Cf. A113877.
Sequence in context: A281399 A043372 A372841 * A223508 A250810 A320893
KEYWORD
nonn
STATUS
approved