A085155 Powers of semiprimes.

1, 4, 6, 9, 10, 14, 15, 16, 21, 22, 25, 26, 33, 34, 35, 36, 38, 39, 46, 49, 51, 55, 57, 58, 62, 64, 65, 69, 74, 77, 81, 82, 85, 86, 87, 91, 93, 94, 95, 100, 106, 111, 115, 118, 119, 121, 122, 123, 129, 133, 134, 141, 142, 143, 145, 146, 155, 158, 159, 161, 166

Offset

1,2

Comments

Numbers of form A001358(i)^j;

m>1 is a term iff A067029(m)=A071178(m) and (A001221(m)=2 or A067029(m) is even).

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Formula

{1} UNION {A001358 semiprimes} UNION {A074985 squares of semiprimes} UNION {cubes of semiprimes} UNION {4th powers of semiprimes} UNION ... - Jonathan Vos Post, Sep 06 2006

Mathematica

Select[Range@ 166, Function[n, Or[n == 1, And[Length@ # == 1, EvenQ@ First@ #], And[Length@ # == 2, SameQ @@ #]] &[FactorInteger[n][[All, -1]]]]] (* Michael De Vlieger, Mar 04 2017 *)

Prog

(PARI) is(n)=my(f=factor(n)[, 2]); #f==0 || (#f==2 && f[1]==f[2]) || (#f==1 && f[1]%2==0) \\ Charles R Greathouse IV, Oct 19 2015
(Python)
from math import isqrt
from sympy import primepi, primerange, integer_nthroot
from oeis_sequences.OEISsequences import bisection
def A085155(n):
    def f(x): return int(n+x-1+sum(((t:=primepi(s:=isqrt(y:=integer_nthroot(x, k)[0])))*(t-1)>>1)-sum(primepi(y//p) for p in primerange(s+1)) for k in range(1, x.bit_length())))
    return bisection(f, n, n) # Chai Wah Wu, Jan 02 2026

Crossrefs

Semiprime analog of A000961 = prime powers.

Cf. A001358, A074985, A085156.

Sequence in context: A300079 A233182 A028260 * A371555 A219786 A302038

Adjacent sequences: A085152 A085153 A085154 * A085156 A085157 A085158

Keyword

nonn

Author

Reinhard Zumkeller, Jun 21 2003

Status

approved